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Square array: A(row,col) = 2^(row-1) * 1+(2*A156552(col)) = A156552(A246278(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
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%I #19 Jan 22 2015 01:30:46

%S 1,3,2,5,6,4,7,10,12,8,9,14,20,24,16,11,18,28,40,48,32,17,22,36,56,80,

%T 96,64,15,34,44,72,112,160,192,128,13,30,68,88,144,224,320,384,256,19,

%U 26,60,136,176,288,448,640,768,512,33,38,52,120,272,352,576,896,1280,1536,1024,23,66,76,104,240,544,704,1152,1792,2560,3072,2048,65,46

%N Square array: A(row,col) = 2^(row-1) * 1+(2*A156552(col)) = A156552(A246278(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

%C Shares with A135764 the property that A001511(n) = k for all terms n on row k and when going downwards in each column, terms grow by doubling.

%H Antti Karttunen, <a href="/A253551/b253551.txt">Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of the array</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A(row,col) = A156552(A246278(row,col)).

%F A(row,col) = A135764(row, A005941(col)). [Is otherwise the same array as A135764, but the column positions have been permuted by A005941.]

%F A(row,col) = 2^(row-1) * ((2*A005941(col)) - 1) = 2^(row-1) * A005408(A156552(col)). [The above expands to this.]

%F As a composition of other permutations:

%F a(n) = A156552(A246278(n+1)). [When all three sequences are interpreted as one-dimensional sequences.]

%e The top left corner of the array:

%e 1, 3, 5, 7, 9, 11, 17, 15, 13, 19, 33, 23, 65, 35, 21,

%e 2, 6, 10, 14, 18, 22, 34, 30, 26, 38, 66, 46, 130, 70, 42,

%e 4, 12, 20, 28, 36, 44, 68, 60, 52, 76, 132, 92, 260, 140, 84,

%e 8, 24, 40, 56, 72, 88, 136, 120, 104, 152, 264, 184, 520, 280, 168,

%e 16, 48, 80, 112, 144,176, 272, 240, 208, 304, 528, 368,1040, 560, 336,

%e ...

%o (Scheme, four alternative definitions)

%o (define (A253551 n) (A156552 (A246278 (+ 1 n))))

%o (define (A253551 n) (A135764bi (A002260 n) (A005941 (A004736 n)))) ;; Code for A135764bi given in A135764.

%o (define (A253551 n) (* (A000079 (- (A002260 n) 1)) (+ -1 (* 2 (A005941 (A004736 n))))))

%o (define (A253551 n) (* (A000079 (- (A002260 n) 1)) (A005408 (A156552 (A004736 n)))))

%Y Inverse: A253552.

%Y Cf. A000079, A001511, A002260, A005408, A004736, A005940, A005941, A156552, A246278.

%Y Differs from A135764 for the first time at n=22, where a(22) = 17, while A135764(22) = 13.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Jan 03 2015