Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Nov 15 2019 09:11:53
%S 1,17,121,769,5681,39121,274345,1922945,13447009,94165777,659108825,
%T 4613711233,32296542097,226073894609,1582520918281,11077645104385,
%U 77543495432897,542804558486545,3799631689665337,26597422073425409
%N A sequence with a(n)/a(n-1) converging to 7, generated from a semi-magic square.
%C 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 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,21,49).
%F 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 G.f.: -x*(7*x+1)^2 / ((7*x-1)*(7*x^2+4*x+1)). [_Colin Barker_, Dec 06 2012]
%F 3*a(n) = 7^n +2 *(-1)^n *A213421(n). - _R. J. Mathar_, Nov 15 2019
%e a(4) = 769 since M^4 * [1 0 0] = [769 824 808].
%t 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 Cf. A094943 uses the same format and operations but with different terms.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, May 25 2004
%E Edited and extended by _Robert G. Wilson v_, May 29 2004