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A155000
a(n) = 8*a(n-1) + 56*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=15.
6
1, 1, 15, 176, 2248, 27840, 348608, 4347904, 54305280, 677924864, 8464494592, 105679749120, 1319449690112, 16473663471616, 205678490419200, 2567953077764096, 32061620085587968, 400298333039493120
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
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
(Magma) I:=[1, 15]; [1] cat [n le 2 select I[n] else 8*(Self(n-1) +7*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 20 2021
(Sage)
def A155000_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-7*x-49*x^2)/(1-8*x-56*x^2) ).list()
A155000_list(30) # G. C. Greubel, Apr 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Jan 18 2009
EXTENSIONS
More terms from Philippe Deléham, Jan 27 2009
STATUS
approved