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%I #14 Jun 11 2022 15:18:34
%S 1,3,14,36,47,246,644,843,4414,11556,15127,79206,207364,271443,
%T 1421294,3720996,4870847,25504086,66770564,87403803,457652254,
%U 1198149156,1568397607,8212236486,21499914244,28143753123,147362604494
%N Denominators of A178381(4*n+1)/A178381(4*n)
%C For the numerators see A179131.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,18,0,0,-1).
%F a(n) = A069705(n-1)*A128052(n) for n>=1.
%F Limit(A179131(n)/A179132(n), n =infinity) = 1+cos(Pi/5) = A296182.
%F a(n) = 18*a(n-3)-a(n-6) for n>6. G.f.: -(3*x^6+6*x^5+7*x^4-18*x^3-14*x^2-3*x-1) / ((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). - _Colin Barker_, Jun 27 2013
%p with(GraphTheory): nmax:=116; P:=9: G:=PathGraph(P): A:= AdjacencyMatrix(G): for n from 0 to nmax do B(n):=A^n; A178381(n):=add(B(n)[1,k],k=1..P); od: for n from 0 to nmax-1 do a(n):= denom(A178381(4*n+1)/A178381(4*n)) od: seq(a(n),n=0..nmax/4-1);
%t LinearRecurrence[{0,0,18,0,0,-1},{1,3,14,36,47,246,644},30] (* _Harvey P. Dale_, Jun 11 2022 *)
%Y Cf. A128052 and A179133.
%K easy,frac,nonn
%O 0,2
%A _Johannes W. Meijer_, Jul 01 2010
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