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%I #15 Apr 19 2015 00:54:11
%S 2,5,3,6,8,4,9,10,15,7,12,16,18,26,11,13,22,31,34,49,19,14,23,41,57,
%T 66,95,35,17,25,42,79,110,130,184,67,20,32,47,81,153,215,258,364,131,
%U 21,38,63,89,159,302,424,514,723,259,24,39,73,120,174,312,599,844,1026,1440,515,27,46,74,143,236,343,620,1192,1683,2050,2876,1027
%N Square array A(row,col) read by antidiagonals: A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(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 A256995.
%C If we assume that a(1) = 1 (but which is not explicitly included here because outside of the array proper), then A256998 gives the inverse permutation.
%H Antti Karttunen, <a href="/A256997/b256997.txt">Table of n, a(n) for n = 2..10441; the first 144 antidiagonals of square array</a>
%F A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(A(row-1,col)).
%e The top left corner of the array:
%e 2, 5, 6, 9, 12, 13, 14, 17, 20, 21, 24, 27
%e 3, 8, 10, 16, 22, 23, 25, 32, 38, 39, 46, 50
%e 4, 15, 18, 31, 41, 42, 47, 63, 73, 74, 88, 97
%e 7, 26, 34, 57, 79, 81, 89, 120, 143, 145, 173, 191
%e 11, 49, 66, 110, 153, 159, 174, 236, 281, 287, 341, 375
%e 19, 95, 130, 215, 302, 312, 343, 467, 558, 568, 677, 743
%e 35, 184, 258, 424, 599, 620, 680, 928, 1111, 1132, 1349, 1479
%e 67, 364, 514, 844, 1192, 1235, 1356, 1852, 2216, 2259, 2693, 2951
%e 131, 723, 1026, 1683, 2380, 2464, 2707, 3697, 4428, 4512, 5381, 5895
%e 259, 1440, 2050, 3360, 4755, 4924, 5408, 7387, 8851, 9020, 10757, 11783
%e ...
%o (Scheme)
%o (define (A256997 n) (if (<= n 1) n (A256997bi (A002260 (- n 1)) (A004736 (- n 1)))))
%o (define (A256997bi row col) (if (= 1 row) (A055938 col) (A005187 (A256997bi (- row 1) col))))
%Y Cf. A005187, A055938 (row 1), A256994 (column 1), A256989 (row index), A256990 (column index).
%Y Inverse: A256998.
%Y Transpose: A256995.
%Y Cf. also A254107, A255557 (variants), A246278 (another thematically similar construction).
%K nonn,tabl
%O 2,1
%A _Antti Karttunen_, Apr 14 2015
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