cp's OEIS Frontend

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.

A092167 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,2) entry of M^n.

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%I A092167 #9 Jun 29 2023 18:40:13
%S A092167 4,26,154,926,5554,33326,199954,1199726,7198354,43190126,259140754,
%T A092167 1554844526,9329067154,55974402926,335846417554,2015078505326,
%U A092167 12090471031954,72542826191726,435256957150354,2611541742902126
%N A092167 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,2) entry of M^n.
%H A092167 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5, 6).
%F A092167 a(n) = (5*6^n + 2*(-1)^n)/7.
%F A092167 A092166 -(-1)^n.
%F A092167 From _R. J. Mathar_, Apr 20 2009: (Start)
%F A092167 a(n) = 5*a(n-1) + 6*a(n-2).
%F A092167 G.f.: 2*x*(2+3*x)/((1+x)*(1-6*x)). (End)
%t A092167 Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[2, 2]], {n, 20}] (* _Robert G. Wilson v_, Apr 22 2004 *)
%Y A092167 Cf. A092164, A092165, A092166.
%K A092167 nonn
%O A092167 1,1
%A A092167 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004
%E A092167 Edited by _Robert G. Wilson v_, Apr 22 2004