A158608 - OEIS

%I #18 Jan 03 2024 08:48:48

%S 1,4,20,84,404,1748,8212,36180,167572,746452,3427604,15370836,

%T 70212500,316145876,1439545876,6497879892,29530613908,133496692180,

%U 605986514708,2741933589588,12437717824916,56308655258324,255312140456980

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

%C 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 H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 221.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,16).

%F a(n) = A168579(n) + 3*A168579(n-1).

%F G.f.: (1+3x)/(1-x-16*x^2). - _Philippe Deléham_, Mar 26 2009

%t Clear[M, v, t, n];

%t M = {{0, t}, {t, 1/t}};

%t v[0] = {1, 1};

%t v[n_] := v[n] = M.v[n - 1];

%t t = 2;

%t a = Table[t^n*v[n][[1]], {n, 0, 30}]

%Y Cf. A168579.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Mar 22 2009

%E Definition simplified following the Deleham proposition of Mar 2009 - The Assoc. Eds. of the OEIS, Aug 29 2010