This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A251721 #14 Apr 01 2017 20:54:24 %S A251721 1,2,1,3,2,1,5,3,2,1,4,4,3,2,1,7,6,4,3,2,1,11,7,5,4,3,2,1,6,9,6,5,4,3, %T A251721 2,1,13,10,7,6,5,4,3,2,1,17,5,8,7,6,5,4,3,2,1,10,12,10,8,7,6,5,4,3,2, %U A251721 1,19,15,11,9,8,7,6,5,4,3,2,1,9,8,13,10,9,8,7,6,5,4,3,2,1,8,16,14,11,10,9,8,7,6,5,4,3,2,1,23,19,15,12,11,10,9,8,7,6,5,4,3,2,1 %N A251721 Square array of permutations: A(row,col) = A249822(row, A249821(row+1, col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... %C A251721 These are the "first differences" between permutations of array A249821, in a sense that by composing the first k rows of this array [from left to right, as in a(n) = row_1(row_2(...(row_k(n))))], one obtains row k+1 of A249821. %C A251721 On row n, the first A250473(n) terms are fixed, and the first non-fixed term comes at A250474(n). %F A251721 A(row,col) = A249822(row, A249821(row+1, col)). %F A251721 A(row,col) = A078898(A246278(row, A246277(A083221(row+1, col)))). %e A251721 The top left corner of the array: %e A251721 1, 2, 3, 5, 4, 7, 11, 6, 13, 17, 10, 19, 9, 8, 23, 29, 14, 15, 31, 22, ... %e A251721 1, 2, 3, 4, 6, 7, 9, 10, 5, 12, 15, 8, 16, 19, 21, 22, 13, 24, 11, 27, ... %e A251721 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 9, 16, 18, 20, 21, 23, 24, ... %e A251721 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, ... %e A251721 ... %o A251721 (Scheme) %o A251721 (define (A251721bi row col) (A249822bi row (A249821bi (+ row 1) col))) %o A251721 (define (A251721 n) (A251721bi (A002260 n) (A004736 n))) %o A251721 ;; Code for A249821bi and A249822bi given in A249821, A249822. %Y A251721 Inverse permutations can be found from array A251722. %Y A251721 Row 1: A064216, Row 2: A249745, Row 3: A250475. %Y A251721 Cf. A000027, A002260, A004736, A078898, A083221, A246277, A246278, A249821, A249822, A250473, A250474. %K A251721 nonn,tabl %O A251721 1,2 %A A251721 _Antti Karttunen_, Dec 07 2014