A155000 - OEIS

A155000

a(n) = 8*a(n-1) + 56*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=15.

1, 1, 15, 176, 2248, 27840, 348608, 4347904, 54305280, 677924864, 8464494592, 105679749120, 1319449690112, 16473663471616, 205678490419200, 2567953077764096, 32061620085587968, 400298333039493120

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OFFSET

0,3

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..900

Index entries for linear recurrences with constant coefficients, signature (8,56).

FORMULA

a(n) = Sum_{k=0..n} A155112(n,k)*7^(n-k). - Philippe Deléham, Jan 27 2009

G.f.: 1 + x*(1+7*x)/(1-8*x-56*x^2). - Harvey P. Dale, Dec 11 2012

MAPLE

m:=30; S:=series( (1-7*x-49*x^2)/(1-8*x-56*x^2), x, m+1):

seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Apr 20 2021

MATHEMATICA

Join[{1}, LinearRecurrence[{8, 56}, {1, 15}, 20]] (* Harvey P. Dale, Dec 11 2012 *)

PROG