A154997 a(n) = 6*a(n-1) + 30*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=11.

1, 1, 11, 96, 906, 8316, 77076, 711936, 6583896, 60861456, 562685616, 5201957376, 48092312736, 444612597696, 4110444968256, 38001047740416, 351319635490176, 3247949245153536, 30027284535626496, 277602184568365056

Offset: 0

Author

Philippe Deléham, Jan 18 2009

Keywords

• nonn

Comments

The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*a(n-2)), with b some constant. The generating function of these is (1 - b*x - b^2*x^2)/(1 - (b+1)*x - b*(1+b)*x^2). - R. J. Mathar, Jan 20 2009

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,30).

Crossrefs

Cf. A154996, A154999, A155000, A155001.

Programs

Magma

I:=[1,11]; [1] cat [n le 2 select I[n] else 6*(Self(n-1) +5*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 21 2021

Maple

m:=30; S:=series( (1-5*x-25*x^2)/(1-6*x-30*x^2), x, m+1):
seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Apr 21 2021

Mathematica

Join[{1},LinearRecurrence[{6,30},{1,11},20]] (* Harvey P. Dale, Feb 07 2012 *)

Sage

def A154996_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-5*x-25*x^2)/(1-6*x-30*x^2) ).list()
A154996_list(30) # G. C. Greubel, Apr 21 2021

Formula

G.f.: (1 -5*x -25*x^2)/(1 -6*x -30*x^2).

a(n+1) = Sum_{k=0..n} A154929(n,k)*5^(n-k).