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A179131 Numerators of A178381(4*n+1)/A178381(4*n) 5

%I #12 Oct 18 2020 04:33:56

%S 1,5,25,65,85,445,1165,1525,7985,20905,27365,143285,375125,491045,

%T 2571145,6731345,8811445,46137325,120789085,158114965,827900705,

%U 2167472185,2837257925,14856075365,38893710245,50912527685,266581455865

%N Numerators of A178381(4*n+1)/A178381(4*n)

%C For the denominators see A179132.

%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) = 5*A167808(2*n+1) 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.: -(4*x^6+5*x^5+5*x^4-47*x^3-25*x^2-5*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):= numer(A178381(4*n+1)/A178381(4*n)) od: seq(a(n),n=0..nmax/4-1);

%Y Cf. A128052, A179133, A179132.

%K easy,frac,nonn

%O 0,2

%A _Johannes W. Meijer_, Jul 01 2010

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)