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%I #22 Sep 20 2016 13:26:19
%S 1,3,2,7,6,4,5,10,12,8,9,22,20,24,16,21,18,28,40,48,64,13,30,36,56,80,
%T 192,32,19,26,60,72,112,160,96,184,25,14,52,120,144,224,640,552,352,
%U 11,46,76,208,240,576,448,320,1056,704,15,58,68,136,104,480,288,1720,1600,2112,1408
%N Square array A(row,col): For row=0, A(0,col) = A265341(col), for row > 0, A(row,col) = A265342(A(row-1,col)).
%C Square array A(row,col) is read by downwards antidiagonals as: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), A(0,3), A(1,2), A(2,1), A(3,0), ...
%C All the terms in the same column are either all divisible by 3, or none of them are.
%C Reducing A265342 to its constituent sequences gives A265342(n) = A263273(2*A263273(n)). Iterating this function k times starting from n reduces to (because A263273 is an involution, so pairs of them are canceled) to A263273((2^k)*A263273(n)).
%H Antti Karttunen, <a href="/A265345/b265345.txt">Table of n, a(n) for n = 1..7381; the antidiagonals 0 .. 120 of the array</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F For row=0, A(0,col) = A265341(col), for row>0, A(row,col) = A265342(A(row-1,col)).
%F A(row, col) = A263273((2^row) * A263273(A265341(col))). [The above reduces to this.]
%e The top left corner of the array:
%e 1, 3, 7, 5, 9, 21, 13, 19, 25, 11, 15, 39, .
%e 2, 6, 10, 22, 18, 30, 26, 14, 46, 58, 66, 78, .
%e 4, 12, 20, 28, 36, 60, 52, 76, 68, 44, 84, 156, .
%e 8, 24, 40, 56, 72, 120, 208, 136, 88, 232, 168, 624, .
%e 16, 48, 80, 112, 144, 240, 104, 200, 496, 424, 336, 312, .
%e 64, 192, 160, 224, 576, 480, 520, 256, 344, 608, 672, 1560, .
%e 32, 96, 640, 448, 288, 1920, 1144, 512, 1984, 736, 1344, 3432, .
%e 184, 552, 320, 1720, 1656, 960, 2072, 1024, 1376, 4384, 5160, 6216, .
%e 352, 1056, 1600, 824, 3168, 4800, 3712, 6040, 5344, 2936, 2472, 11136, .
%e ...
%o (Scheme)
%o (define (A265345 n) (A265345bi (A002262 (+ -1 n)) (A025581 (+ -1 n)))) ;; o=1.
%o (define (A265345bi row col) (A263273 (* (A000079 row) (A263273 (A265341 col))))) ;; Faster than below.
%o (define (A265345bi row col) (if (= 0 row) (A265341 col) (A265342 (A265345bi (- row 1) col)))) ;; row>=0, col>=0.
%Y Inverse: A265346.
%Y Transpose: A265347.
%Y Leftmost column: A264980.
%Y Topmost row: A265341.
%Y Row index: A265330 (zero-based), A265331 (one-based).
%Y Column index: A265910 (zero-based), A265911 (one-based).
%Y Cf. also A265342.
%Y Related permutations: A263273, A265895.
%K nonn,tabl,base
%O 1,2
%A _Antti Karttunen_, Dec 18 2015
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