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A256997 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)).

%I A256997 #15 Apr 19 2015 00:54:11
%S A256997 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 A256997 66,95,35,17,25,42,79,110,130,184,67,20,32,47,81,153,215,258,364,131,
%U A256997 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 A256997 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 A256997 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 A256997 This is transpose of array A256995.
%C A256997 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 A256997 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 A256997 A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(A(row-1,col)).
%e A256997 The top left corner of the array:
%e A256997     2,    5,    6,    9,   12,   13,   14,   17,   20,   21,    24,    27
%e A256997     3,    8,   10,   16,   22,   23,   25,   32,   38,   39,    46,    50
%e A256997     4,   15,   18,   31,   41,   42,   47,   63,   73,   74,    88,    97
%e A256997     7,   26,   34,   57,   79,   81,   89,  120,  143,  145,   173,   191
%e A256997    11,   49,   66,  110,  153,  159,  174,  236,  281,  287,   341,   375
%e A256997    19,   95,  130,  215,  302,  312,  343,  467,  558,  568,   677,   743
%e A256997    35,  184,  258,  424,  599,  620,  680,  928, 1111, 1132,  1349,  1479
%e A256997    67,  364,  514,  844, 1192, 1235, 1356, 1852, 2216, 2259,  2693,  2951
%e A256997   131,  723, 1026, 1683, 2380, 2464, 2707, 3697, 4428, 4512,  5381,  5895
%e A256997   259, 1440, 2050, 3360, 4755, 4924, 5408, 7387, 8851, 9020, 10757, 11783
%e A256997   ...
%o A256997 (Scheme)
%o A256997 (define (A256997 n) (if (<= n 1) n (A256997bi (A002260 (- n 1)) (A004736 (- n 1)))))
%o A256997 (define (A256997bi row col) (if (= 1 row) (A055938 col) (A005187 (A256997bi (- row 1) col))))
%Y A256997 Cf. A005187, A055938 (row 1), A256994 (column 1), A256989 (row index), A256990 (column index).
%Y A256997 Inverse: A256998.
%Y A256997 Transpose: A256995.
%Y A256997 Cf. also A254107, A255557 (variants), A246278 (another thematically similar construction).
%K A256997 nonn,tabl
%O A256997 2,1
%A A256997 _Antti Karttunen_, Apr 14 2015