%I #19 Apr 01 2017 20:55:44

%S 1,2,1,4,2,1,3,4,2,1,6,3,4,2,1,6,8,3,4,2,1,10,6,8,3,4,2,1,5,12,6,8,3,

%T 4,2,1,12,5,16,6,8,3,4,2,1,9,9,5,16,6,8,3,4,2,1,14,12,9,5,16,6,8,3,4,

%U 2,1,10,20,12,9,5,16,6,8,3,4,2,1,22,10,24,12,9,5,16,6,8,3,4,2,1,15,28,10,32,12,9,5,16,6,8,3,4,2,1,18,18,40,10,32,12,9,5,16,6,8,3,4,2,1

%N Square array read by antidiagonals: rows are successively recursivized versions of Bulgarian solitaire operation (starting from the usual "first order" version, A242424), as applied to the partitions listed in A112798.

%C The array is read by antidiagonals: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... .

%C Please see comments and references in A242424 for more information about Bulgarian Solitaire.

%C Each row is a A241909-conjugate of the corresponding row in A243060.

%C Rows in both arrays converge towards A122111.

%C All the terms in column n are multiples of A105560(n).

%C The rows of this table (i.e., the corresponding functions) preserve A056239.

%C First point where row k differs from row k of A243060 seems to be A000040(k+2): primes from five onward: 5, 7, 11, 13, 17, 19, 23, 29, 31, ... and these seem to be also the points where that row differs for the first time from A122111.

%H Antti Karttunen, <a href="/A243070/b243070.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the square array</a>

%F A(1,col) = A242424(col), otherwise, when row > 1, A(row,col) = A000040(A001222(col)) * A(row-1, A064989(col)).

%e The top left corner of the array is:

%e 1, 2, 4, 3, 6, 6, 10, 5, 12, 9, 14, 10, 22, 15, 18, ...

%e 1, 2, 4, 3, 8, 6, 12, 5, 9, 12, 20, 10, 28, 18, 18, ...

%e 1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 24, 10, 40, 24, 18, ...

%e 1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 48, 24, 18, ...

%e 1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 64, 24, 18, ...

%o (Scheme)

%o (define (A243070 n) (A243070bi (A002260 n) (A004736 n)))

%o (define (A243070bi row col) (cond ((<= col 1) col) ((= 1 row) (A242424 col)) (else (* (A000040 (A001222 col)) (A243070bi (- row 1) (A064989 col))))))

%Y Row 1: A242424, Row 2: A243072, Row 3: A243073.

%Y Rows converge towards A122111.

%Y Cf. A243060, A241909, A112798, A105560, A000040, A001222, A064989.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, May 29 2014