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%I #5 Jul 03 2023 11:11:44
%S 1,4,16,68,272,1092,4624,18500,74512,314436,1258512,5083204,21382416,
%T 85627972,346707472,1454102596,5826897680,23643380804,98889463824,
%U 396564832324,1612065835280,6725490517060,26992215104016
%N a(n)=a(n-2)+64*a(n-3) with a(0)=1, a(1)=4, a(3)=16.
%C The sequence is also 2^n times the sum of the three top-row entries
%C of the n-th power of the matrix (0,2,0; 0,0,2;, 2,1/8,0) .
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 64).
%F G.f.: -(1+4*x+15*x^2)/(-1+x^2+64*x^3). [From _R. J. Mathar_, Mar 26 2009]
%t Clear[M, v, t, n];
%t M = {{0, t, 0}, {0, 0, t}, {t, 1/t^3, 0}};
%t v[0] = {1, 1, 1};
%t v[n_] := v[n] = M.v[n - 1];
%t CharacteristicPolynomial[M, x];
%t t = 2; a = Table[t^n*v[n][[1]], {n, 0, 30}]
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, Mar 25 2009
%E Definition replaced by recurrence - The Associate Editors of the OEIS - Oct 05 2009
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