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Square array A(row,col) read by antidiagonals: A(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).
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%I #13 Apr 19 2015 00:53:54

%S 2,3,5,4,8,6,7,15,10,9,11,26,18,16,12,19,49,34,31,22,13,35,95,66,57,

%T 41,23,14,67,184,130,110,79,42,25,17,131,364,258,215,153,81,47,32,20,

%U 259,723,514,424,302,159,89,63,38,21,515,1440,1026,844,599,312,174,120,73,39,24,1027,2876,2050,1683,1192,620,343,236,143,74,46,27

%N Square array A(row,col) read by antidiagonals: A(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).

%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 A256997.

%C If we assume that a(1) = 1 (but which is not explicitly included here because outside of the array proper), then A256996 gives the inverse permutation.

%H Antti Karttunen, <a href="/A256995/b256995.txt">Table of n, a(n) for n = 2..10441; the first 144 antidiagonals of square array</a>

%F A(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).

%e The top left corner of the array:

%e 2, 3, 4, 7, 11, 19, 35, 67, 131, 259, 515, 1027

%e 5, 8, 15, 26, 49, 95, 184, 364, 723, 1440, 2876, 5745

%e 6, 10, 18, 34, 66, 130, 258, 514, 1026, 2050, 4098, 8194

%e 9, 16, 31, 57, 110, 215, 424, 844, 1683, 3360, 6716, 13425

%e 12, 22, 41, 79, 153, 302, 599, 1192, 2380, 4755, 9504, 19004

%e 13, 23, 42, 81, 159, 312, 620, 1235, 2464, 4924, 9841, 19675

%e 14, 25, 47, 89, 174, 343, 680, 1356, 2707, 5408, 10812, 21617

%e 17, 32, 63, 120, 236, 467, 928, 1852, 3697, 7387, 14765, 29521

%e 20, 38, 73, 143, 281, 558, 1111, 2216, 4428, 8851, 17696, 35388

%e 21, 39, 74, 145, 287, 568, 1132, 2259, 4512, 9020, 18033, 36059

%e ...

%o (Scheme)

%o (define (A256995 n) (if (<= n 1) n (A256995bi (A002260 (- n 1)) (A004736 (- n 1)))))

%o (define (A256995bi row col) (if (= 1 col) (A055938 row) (A005187 (A256995bi row (- col 1)))))

%Y Inverse permutation: A256996.

%Y Transpose: A256997.

%Y Cf. A005187, A055938 (column 1), A256994 (row 1), A256989 (column index), A256990 (row index).

%Y Cf. also A254105, A255555 (variants), A114537, A246279 (other thematically similar constructions).

%K nonn,tabl

%O 2,1

%A _Antti Karttunen_, Apr 14 2015