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

1, 5, 25, 65, 85, 445, 1165, 1525, 7985, 20905, 27365, 143285, 375125, 491045, 2571145, 6731345, 8811445, 46137325, 120789085, 158114965, 827900705, 2167472185, 2837257925, 14856075365, 38893710245, 50912527685, 266581455865

Offset: 0

Author

Johannes W. Meijer, Jul 01 2010

Keywords

• easy
• frac
• nonn

Comments

For the denominators see A179132.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,18,0,0,-1).

Crossrefs

Cf. A128052, A179133, A179132.

Programs

Maple

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);

Formula

a(n) = 5*A167808(2*n+1) for n>=1.

Limit(A179131(n)/A179132(n), n =infinity) = 1+cos(Pi/5) = A296182.

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