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A158608 a(n) = a(n-1) + 16*a(n-2), starting a(0)=1, a(1)=4.

%I A158608 #18 Jan 03 2024 08:48:48
%S A158608 1,4,20,84,404,1748,8212,36180,167572,746452,3427604,15370836,
%T A158608 70212500,316145876,1439545876,6497879892,29530613908,133496692180,
%U A158608 605986514708,2741933589588,12437717824916,56308655258324,255312140456980
%N A158608 a(n) = a(n-1) + 16*a(n-2), starting a(0)=1, a(1)=4.
%C A158608 Quadratic equation associated with group [3,3,5] which instead of t=phi uses t=2 in Phi(t) = (1 + sqrt(1+4*t^4))/(2*t).
%D A158608 H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 221.
%H A158608 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,16).
%F A158608 a(n) = A168579(n) + 3*A168579(n-1).
%F A158608 G.f.: (1+3x)/(1-x-16*x^2). - _Philippe Deléham_, Mar 26 2009
%t A158608 Clear[M, v, t, n];
%t A158608 M = {{0, t}, {t, 1/t}};
%t A158608 v[0] = {1, 1};
%t A158608 v[n_] := v[n] = M.v[n - 1];
%t A158608 t = 2;
%t A158608 a = Table[t^n*v[n][[1]], {n, 0, 30}]
%Y A158608 Cf. A168579.
%K A158608 nonn,easy
%O A158608 0,2
%A A158608 _Roger L. Bagula_, Mar 22 2009
%E A158608 Definition simplified following the Deleham proposition of Mar 2009 - The Assoc. Eds. of the OEIS, Aug 29 2010