OFFSET
0,1
COMMENTS
Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->0010, 01->011, 10->010, starting with 00; see A289128.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-2,2).
FORMULA
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 2*a(n-4) + 2*a(n-5) for n >= 6, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 28.
From Colin Barker, Jul 02 2017: (Start)
G.f.: (2 + 2*x - 3*x^2 - 2*x^3 + 2*x^4 + 2*x^5) / ((1 - x)^2*(1 + x)*(1 - 2*x^2)).
a(n) = -(3*n)/2 + 7*2^(n/2) - 4 for n>0 and even.
a(n) = (-3*n + 5*2^((n + 3)/2) - 9) / 2 for n odd.
(End)
MATHEMATICA
Join[{2}, LinearRecurrence[{1, 3, -3, -2, 2}, {4, 7, 11, 18, 28}, 40]]
PROG
(PARI) Vec((2 + 2*x - 3*x^2 - 2*x^3 + 2*x^4 + 2*x^5) / ((1 - x)^2*(1 + x)*(1 - 2*x^2)) + O(x^50)) \\ Colin Barker, Jul 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 28 2017
STATUS
approved