A199149 -id:A199149

A199142

Number of n X 1 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.

+10
3

0, 1, 1, 2, 3, 6, 11, 23, 47, 102, 221, 492, 1099, 2485, 5637, 12858, 29391, 67354, 154539, 355003, 816035, 1876862, 4318201, 9937840, 22874731, 52659593, 121237417, 279141170, 642732027, 1479959118, 3407837387, 7847200511

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Column 1 of A199149.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + a(n-4) + 3*a(n-5) for n>6.

Empirical g.f.: x^2*(1 - 2*x - 2*x^2 + 3*x^3 + x^4) / ((1 - x)*(1 - x - x^2)*(1 - x - 3*x^2)). - Colin Barker, Feb 22 2018

EXAMPLE

Some solutions for n=8:

..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

..1....0....0....1....1....1....0....1....1....0....1....0....0....0....1....0

..1....1....0....1....1....1....1....1....1....0....1....0....0....0....1....0

..2....1....1....1....1....0....1....2....1....0....2....1....0....1....1....0

..2....1....1....0....2....0....0....2....1....1....2....1....0....1....1....0

..2....0....0....0....2....1....0....1....0....1....3....1....0....2....2....1

CROSSREFS

Cf. A199149.

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 03 2011

STATUS

approved

A199143

Number of nX2 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
1

1, 3, 13, 65, 393, 2539, 16866, 113432, 766473, 5188597, 35148945, 238173743, 1614066774, 10938730576, 74134306725, 502428413393, 3405102418833, 23077383280435, 156402287318610, 1059984943413152, 7183834447992225

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 2 of A199149

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 7*a(n-1) +2*a(n-2) -16*a(n-3) -49*a(n-4) -35*a(n-5) +56*a(n-6) +54*a(n-7) +45*a(n-8) -27*a(n-9) for n>11

EXAMPLE

Some solutions for n=4

..0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..1....0..1....0..0

..0..1....0..0....1..2....1..0....0..1....0..1....1..0....0..1....0..1....0..1

..1..1....1..1....1..2....1..0....1..1....0..1....1..0....1..2....0..0....0..1

..0..0....0..0....1..1....1..1....2..2....1..1....1..0....1..2....1..1....0..1

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved

A199144

Number of nX3 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
1

1, 13, 132, 2453, 42420, 794416, 14511531, 268456338, 4940928443, 91146218920, 1679743067872, 30969409565822, 570877041856787, 10524153072061784, 194006638767664141, 3576453618832667684, 65930406443303698229

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Column 3 of A199149

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 14*a(n-1) +120*a(n-2) -646*a(n-3) -1320*a(n-4) +3562*a(n-5) +12682*a(n-6) +1896*a(n-7) -76623*a(n-8) +36670*a(n-9) +19724*a(n-10) -245388*a(n-11) +53233*a(n-12) +2738818*a(n-13) -138967*a(n-14) -11411168*a(n-15) +3626519*a(n-16) +17979294*a(n-17) -10633666*a(n-18) -27553810*a(n-19) +19090457*a(n-20) +20077526*a(n-21) -32139160*a(n-22) +46609580*a(n-23) +115127457*a(n-24) +146403730*a(n-25) +50426678*a(n-26) -122760336*a(n-27) -143444310*a(n-28) -587979162*a(n-29) -679787397*a(n-30) -166474764*a(n-31) -212565465*a(n-32) +6372918*a(n-33) +256248603*a(n-34) +47278566*a(n-35) -708588*a(n-36) -12754584*a(n-37) for n>38

EXAMPLE

Some solutions for n=4

..0..1..1....0..1..1....0..1..1....0..0..0....0..1..1....0..0..1....0..0..0

..0..1..2....0..0..0....0..2..0....0..1..1....0..2..2....2..2..1....1..1..0

..3..3..2....2..2..0....2..2..0....2..3..2....1..0..3....1..1..0....0..0..1

..1..1..1....3..3..3....2..0..0....2..3..2....1..0..3....2..2..0....0..1..1

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved

A199145

Number of nX4 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
1

2, 65, 2453, 125468, 6235011, 316561994, 15958823113, 806680624447, 40736752748774, 2057896226081573, 103945296750116087, 5250572116269762125, 265216743260845702081, 13396704712673136390007, 676696655003807234547723

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 4 of A199149

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

EXAMPLE

Some solutions for n=3

..0..0..1..1....0..0..1..1....0..1..1..1....0..1..0..0....0..0..1..1

..2..2..2..3....1..2..3..1....0..2..3..0....0..1..0..2....0..0..2..2

..0..0..3..3....1..2..3..3....0..2..3..0....1..1..2..2....2..2..0..0

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved

A199146

Number of nX5 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
1

3, 393, 42420, 6235011, 839006010, 117380324984, 16158623337745, 2239304268913257, 309471298054332806, 42818034223579225138, 5921413251810033475103, 819050117505774849777870

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 5 of A199149

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..28

EXAMPLE

Some solutions for n=3

..0..0..0..0..1....0..0..1..1..1....0..0..1..1..1....0..0..1..0..0

..2..1..2..2..1....2..0..3..3..1....2..1..1..2..3....2..2..1..1..1

..2..1..2..1..1....2..3..3..2..2....2..0..0..2..3....0..0..2..2..2

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved

A199141

Number of n X n 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
0

0, 3, 132, 125468, 839006010, 44832664800117

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Diagonal of A199149

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

Some solutions for n=4

..0..0..1..1....0..0..1..1....0..0..1..1....0..1..1..1....0..0..1..1

..1..1..0..0....2..2..3..3....1..1..1..0....0..0..2..2....2..3..3..0

..2..2..0..3....2..2..0..0....2..0..0..0....2..2..3..2....2..0..0..0

..0..0..3..3....0..0..2..2....2..2..2..2....1..1..3..2....3..3..3..3

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved

A199147

Number of nX6 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
0

6, 2539, 794416, 316561994, 117380324984, 44832664800117, 16925667317073175

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 6 of A199149

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

Some solutions for n=3

..0..1..1..1..1..2....0..0..1..2..3..3....0..1..0..0..2..2....0..0..1..1..1..2

..0..1..0..2..1..2....0..1..1..2..0..3....0..1..1..0..2..2....1..1..3..3..0..2

..0..1..0..2..1..1....0..0..0..0..0..3....0..0..1..3..3..3....1..1..0..0..0..2

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved

A199148

Number of nX7 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

+10
0

11, 16866, 14511531, 15958823113, 16158623337745, 16925667317073175

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 7 of A199149

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

Some solutions for n=3

..0..0..1..2..2..0..1....0..0..0..1..2..0..0....0..0..1..0..2..3..0

..0..1..1..3..0..0..1....0..1..0..1..2..2..2....0..1..1..0..2..3..0

..0..0..3..3..2..2..1....0..1..0..1..1..3..3....0..0..0..0..1..1..0

KEYWORD

nonn

AUTHOR

R. H. Hardin Nov 03 2011

STATUS

approved