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A179131 Numerators of A178381(4*n+1)/A178381(4*n) 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For the denominators see A179132.

LINKS

Table of n, a(n) for n=0..26.

FORMULA

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

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

Conjecture: 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

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);

CROSSREFS

Cf. A128052 and A179133.

Sequence in context: A182211 A146404 A323187 * A054994 A108403 A007058

Adjacent sequences:  A179128 A179129 A179130 * A179132 A179133 A179134

KEYWORD

easy,frac,nonn

AUTHOR

Johannes W. Meijer, Jul 01 2010

STATUS

approved

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)