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 A261880 #34 Aug 08 2016 17:30:13 %S A261880 1,-1,-2,1,2,4,-2,-3,-5,-9,5,7,10,15,24,-16,-21,-28,-38,-53,-77,61,77, %T A261880 98,126,164,217,294,-272,-333,-410,-508,-634,-798,-1015,-1309,1385, %U A261880 1657,1990,2400,2908,3542,4340,5355,6664 %N A261880 Array of higher-order differences of the sequence (-1)^n*A000111(n) read by downward antidiagonals. %C A261880 Difference array of (-1)^n*A000111(n): %C A261880 1, -1, 1, -2, 5, ... %C A261880 -2, 2, -3, 7,... %C A261880 4, -5, 10, ... %C A261880 -9, 15, ... %C A261880 24, ... . %C A261880 First column:(-1)^n*A000667(n). %C A261880 Antidiagonal sums: b(n) = 1, -3, 7, -19, 61, -233, 1037, -5279, 30241, ..., i.e., row sums of the triangle. %C A261880 Any triangle with entries T(n, m) built from some sequence in column m=0, and the recurrence T(n, m) = T(n, m-1) - T(n-1, m-1) for m >= 1, has the property that the new triangle t(n, m) = T(n+1, m+1) - T(n+1, m), 0 <= m <= n, equals -T(n, m). See the question in the example. - _Wolfdieter Lang_, Aug 08 2016 %F A261880 Recurrence: T(n, 0) = (-1)^n*A000111(n), n >= 0. T(n, m) = T(n, m-1) - T(n-1, m-1), m >= 1. (from the fact that the differences of the rows, starting with n = 1 produce the negative of the triangle. See the example and a comment). - _Wolfdieter Lang_, Aug 08 2016 %e A261880 The triangle T(n, m) begins: %e A261880 n\m 0 1 2 3 4 5 ... %e A261880 0: 1 %e A261880 1: -1 -2 %e A261880 2: 1 2 4 %e A261880 3: -2 -3 -5 -9 %e A261880 4: 5 7 10 15 24, %e A261880 5: -16 -21 -28 -38 -53 -77 %e A261880 ... %e A261880 Triangle of differences of the row entries of the preceding triangle starting with row n=1: %e A261880 n\m 0 1 2 3 4 ... %e A261880 0: -1 %e A261880 1: 1 2 %e A261880 2: -1 -2 -4 %e A261880 3: 2 3 5 9 %e A261880 4: -5 -7 -10 -15 -24 %e A261880 ... . %e A261880 This is the negative of the first triangle. Are there other sequences with the same property? %Y A261880 Cf. A000111, A000667, A062162, A227862, A239005. %K A261880 sign,tabl %O A261880 0,3 %A A261880 _Paul Curtz_, Jul 10 2016 %E A261880 Edited by _Wolfdieter Lang_, Aug 08 2016