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%I #15 Mar 16 2024 14:25:12
%S 5,25,155,925,5555,33325,199955,1199725,7198355,43190125,259140755,
%T 1554844525,9329067155,55974402925,335846417555,2015078505325,
%U 12090471031955,72542826191725,435256957150355,2611541742902125
%N Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,1) entry of M^n.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,6).
%F a(n) = (5*6^n - 5*(-1)^n)/7.
%F a(n) = A092167(n) +(-1)^n.
%F From _Colin Barker_, Nov 08 2012: (Start)
%F a(n) = 5*a(n-1) + 6*a(n-2).
%F G.f.: -5*x/((x+1)*(6*x-1)). (End)
%t Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[2, 1]], {n, 20}] (* _Robert G. Wilson v_, Apr 22 2004 *)
%Y Cf. A092164, A092165, A092167.
%K nonn,easy
%O 1,1
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004
%E Edited by _Robert G. Wilson v_, Apr 22 2004
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