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%I #15 Apr 19 2015 00:52:47
%S 1,2,3,5,4,7,6,10,8,15,9,11,19,16,31,12,18,22,38,32,63,13,23,35,42,74,
%T 64,127,14,25,46,70,82,146,128,255,17,26,49,89,138,162,290,256,511,20,
%U 34,50,97,176,274,322,578,512,1023,21,39,67,98,193,350,546,642,1154,1024,2047,24,41,78,134,194,385,695,1090,1282,2306,2048,4095
%N Square array A(row,col): A(1,1) = 1, A(1,col) = A055938(col-1), and for row > 1: A(row,col) = A005187(1+A(row-1,col)).
%C The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
%C This is transpose of array A255555, see comments and links given there.
%H Antti Karttunen, <a href="/A255557/b255557.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A(row,col): A(1,1) = 1, and for the rest of topmost row: A(1,col) = A055938(col-1), and for any row > 1: A(row,col) = A005187(1+A(row-1,col)).
%e The top left corner of the array:
%e 1, 2, 5, 6, 9, 12, 13, 14, 17, 20, 21, 24
%e 3, 4, 10, 11, 18, 23, 25, 26, 34, 39, 41, 47
%e 7, 8, 19, 22, 35, 46, 49, 50, 67, 78, 81, 94
%e 15, 16, 38, 42, 70, 89, 97, 98, 134, 153, 161, 184
%e 31, 32, 74, 82, 138, 176, 193, 194, 266, 304, 321, 365
%e 63, 64, 146, 162, 274, 350, 385, 386, 530, 606, 641, 726
%e 127, 128, 290, 322, 546, 695, 769, 770, 1058, 1207, 1281, 1447
%e 255, 256, 578, 642, 1090, 1387, 1537, 1538, 2114, 2411, 2561, 2891
%e 511, 512, 1154, 1282, 2178, 2770, 3073, 3074, 4226, 4818, 5121, 5778
%e 1023, 1024, 2306, 2562, 4354, 5535, 6145, 6146, 8450, 9631, 10241, 11551
%e ...
%o (Scheme)
%o (define (A255557 n) (A255555bi (A004736 n) (A002260 n)))
%o (define (A255555bi row col) (if (= 1 col) (if (= 1 row) 1 (A055938 (- row 1))) (A005187 (+ 1 (A255555bi row (- col 1))))))
%Y Inverse permutation: A255558.
%Y Transpose: A255555.
%Y Column 1: A000225.
%Y Cf. A005187, A055938.
%Y Cf. A255559 (row index), A255560 (column index).
%Y Cf. also A254107, A256997 (variants).
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Apr 13 2015
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