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 A379048 #7 Mar 31 2025 07:00:04
%S A379048 1,1,2,2,-1,3,6,-3,-1,4,19,4,-1,8,40,-60,-40,8,1,13,104,-260,-260,104,
%T A379048 13,-1,21,273,-1092,-1820,1092,273,-21,-1,33,747,-3894,-16270,-3894,
%U A379048 747,33,-1,55,1870,-19635,-85085,136136,85085,-19635,-1870,55,1,89
%N A379048 Irregular triangular array: row n is the linear recurrence signature of F(i)^n - F(i-1)^n, where F = A000045 (Fibonacci numbers).
%C A379048 (column 1) = (1, 2, 3, 4, 8, 13, 21, 33, 55, 89, 144, 232, ...) is linearly recurrent with signature (1,1,0,1,-1,-1).
%C A379048 (column 2) = (1, 2, 6, 19, 40, 104, 273, 747, 1870, 4895, 12816, 33784, ...) is linearly recurrent with signature (3, -1, 0, 8, -24, 8, 0, -8, 24, -8, 0, 1, -3, 1).
%C A379048 Row n is also the linear recurrence signature of L(i)^n - L(i-1)^n, where L = A000032 (Lucas numbers).
%F A379048 First 10 rows:
%F A379048 1 1
%F A379048 2 2 -1
%F A379048 3 6 -3 -1
%F A379048 4 19 4 -1
%F A379048 8 40 -60 -40 8 1
%F A379048 13 104 -260 -260 104 13 -1
%F A379048 21 273 -1092 -1820 1092 273 -21 -1
%F A379048 33 747 -3894 -16270 -3894 747 33 -1
%F A379048 55 1870 -19635 -85085 136136 85085 -19635 -1870 55 1
%F A379048 89 4895 -83215 -582505 1514513 1514513 -582505 -83215 4895 89 -1
%t A379048 z = 25; w[i_] := Fibonacci[i];
%t A379048 t[p_] := Table[w[i]^p - w[i - 1]^p, {i, 1, z}];
%t A379048 Column[Table[FindLinearRecurrence[t[p]], {p, 1, 12}]] (* array *)
%t A379048 Flatten[Table[FindLinearRecurrence[t[p]], {p, 1, 12}]] (* sequence *)
%Y A379048 Cf. A000032, A000045, A226205, A346513.
%K A379048 sign,tabf
%O A379048 1,3
%A A379048 _Clark Kimberling_, Dec 16 2024