A179132 Denominators of A178381(4*n+1)/A178381(4*n).

1, 3, 14, 36, 47, 246, 644, 843, 4414, 11556, 15127, 79206, 207364, 271443, 1421294, 3720996, 4870847, 25504086, 66770564, 87403803, 457652254, 1198149156, 1568397607, 8212236486, 21499914244, 28143753123, 147362604494

Offset: 0

Author

Johannes W. Meijer, Jul 01 2010

Keywords

• easy
• frac
• nonn

Comments

For the numerators see A179131.

Links

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

Crossrefs

Cf. A128052 and A179133.

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):= denom(A178381(4*n+1)/A178381(4*n)) od: seq(a(n),n=0..nmax/4-1);

Mathematica

LinearRecurrence[{0,0,18,0,0,-1},{1,3,14,36,47,246,644},30] (* Harvey P. Dale, Jun 11 2022 *)

Formula

a(n) = A069705(n-1)*A128052(n) 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.: -(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