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A243070 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.

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%I A243070 #19 Apr 01 2017 20:55:44
%S A243070 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 A243070 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 A243070 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 A243070 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 A243070 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 A243070 Please see comments and references in A242424 for more information about Bulgarian Solitaire.
%C A243070 Each row is a A241909-conjugate of the corresponding row in A243060.
%C A243070 Rows in both arrays converge towards A122111.
%C A243070 All the terms in column n are multiples of A105560(n).
%C A243070 The rows of this table (i.e., the corresponding functions) preserve A056239.
%C A243070 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 A243070 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 A243070 A(1,col) = A242424(col), otherwise, when row > 1, A(row,col) = A000040(A001222(col)) * A(row-1, A064989(col)).
%e A243070 The top left corner of the array is:
%e A243070   1,  2,  4,  3,  6,  6, 10,  5, 12,  9, 14, 10, 22, 15, 18, ...
%e A243070   1,  2,  4,  3,  8,  6, 12,  5,  9, 12, 20, 10, 28, 18, 18, ...
%e A243070   1,  2,  4,  3,  8,  6, 16,  5,  9, 12, 24, 10, 40, 24, 18, ...
%e A243070   1,  2,  4,  3,  8,  6, 16,  5,  9, 12, 32, 10, 48, 24, 18, ...
%e A243070   1,  2,  4,  3,  8,  6, 16,  5,  9, 12, 32, 10, 64, 24, 18, ...
%o A243070 (Scheme)
%o A243070 (define (A243070 n) (A243070bi (A002260 n) (A004736 n)))
%o A243070 (define (A243070bi row col) (cond ((<= col 1) col) ((= 1 row) (A242424 col)) (else (* (A000040 (A001222 col)) (A243070bi (- row 1) (A064989 col))))))
%Y A243070 Row 1: A242424, Row 2: A243072, Row 3: A243073.
%Y A243070 Rows converge towards A122111.
%Y A243070 Cf. A243060, A241909, A112798, A105560, A000040, A001222, A064989.
%K A243070 nonn,tabl
%O A243070 1,2
%A A243070 _Antti Karttunen_, May 29 2014