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A155000
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a(n) = 8*a(n-1) + 56*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=15.
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6
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1, 1, 15, 176, 2248, 27840, 348608, 4347904, 54305280, 677924864, 8464494592, 105679749120, 1319449690112, 16473663471616, 205678490419200, 2567953077764096, 32061620085587968, 400298333039493120
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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MAPLE
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m:=30; S:=series( (1-7*x-49*x^2)/(1-8*x-56*x^2), x, m+1):
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MATHEMATICA
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Join[{1}, LinearRecurrence[{8, 56}, {1, 15}, 20]] (* Harvey P. Dale, Dec 11 2012 *)
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PROG
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(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)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-7*x-49*x^2)/(1-8*x-56*x^2) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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