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 A094944 #17 Jan 05 2025 23:38:09
%S A094944 1,17,121,769,5681,39121,274345,1922945,13447009,94165777,659108825,
%T A094944 4613711233,32296542097,226073894609,1582520918281,11077645104385,
%U A094944 77543495432897,542804558486545,3799631689665337,26597422073425409
%N A094944 A sequence with a(n)/a(n-1) converging to 7, generated from a semi-magic square.
%C A094944 3 rows: 1 4 2, 2 1 4, 4 2 1 form a semi-magic square: row sums and columns and the diagonal = 7, the convergent of the sequence.
%H A094944 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,21,49).
%F A094944 Let M = the 3 X 3 matrix [1 4 2 / 2 1 4 / 4 2 1], then with M^n * [1 0 0] = [p q r], a(n) = p.
%F A094944 G.f.: -x*(7*x+1)^2 / ((7*x-1)*(7*x^2+4*x+1)). [_Colin Barker_, Dec 06 2012]
%F A094944 3*a(n) = 7^n +2 *(-1)^n *A213421(n). - _R. J. Mathar_, Nov 15 2019
%e A094944 a(4) = 769 since M^4 * [1 0 0] = [769 824 808].
%t A094944 a[n_] := (MatrixPower[{{1, 4, 2}, {2, 1, 4}, {4, 2, 1}}, n].{{1}, {0}, {0}})[[1, 1]]; Table[ a[n], {n, 10}] (* _Robert G. Wilson v_, May 29 2004 *)
%Y A094944 Cf. A094943 uses the same format and operations but with different terms.
%K A094944 nonn,easy
%O A094944 1,2
%A A094944 _Gary W. Adamson_, May 25 2004
%E A094944 Edited and extended by _Robert G. Wilson v_, May 29 2004