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 A109518 #2 Mar 30 2012 17:34:19
%S A109518 1,3,38,783,22480,828000,37231704,1977187485,121098539008,
%T A109518 8403438270285,651608685100000,55835951178466800,5239593453691293696,
%U A109518 534383614812622168191,58857325474654519917440
%N A109518 a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;n-1,3(n-1)].
%C A109518 The (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;1,1] is the Fibonacci number A000045(n).
%e A109518 a(4)=783 because if M is the 2 X 2 matrix [0,1;3,9], then M^4 is the 2 X 2 matrix [252,783,2349,7299].
%p A109518 with(linalg): a:=proc(n) local A,k: A[1]:=matrix(2,2,[0,1,n-1,3*(n-1)]): for k from 2 to n do A[k]:=multiply(A[k-1],A[1]) od: A[n][1,2] end: seq(a(n),n=1..18);
%t A109518 M[n_] = If[n > 1, MatrixPower[{{0, 1}, {n - 1, 3*(n - 1)}}, n], {{0, 1}, {1, 1}}] a = Table[M[n][[1, 2]], {n, 1, 50}]
%Y A109518 Cf. A000045, A000166.
%K A109518 nonn
%O A109518 1,2
%A A109518 _Roger L. Bagula_, Jun 16 2005