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A155001
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a(n) = 9*a(n-1) + 72*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=17.
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6
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1, 1, 17, 225, 3249, 45441, 642897, 9057825, 127809009, 1802444481, 25424248977, 358594243425, 5057894117169, 71339832581121, 1006226869666257, 14192509772837025, 200180922571503729, 2823489006787799361
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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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a(n+1) = Sum_{k=0..n} A154929(n,k)*8^(n-k).
G.f.: (1 - 8*x - 64*x^2)/(1 - 9*x - 72*x^2). - G. C. Greubel, Apr 20 2021
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MAPLE
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a[0] := 1: a[1] := 1: a[2] := 17: for n from 3 to 25 do a[n] := 9*a[n-1]+72*a[n-2] end do: seq(a[n], n = 0 .. 17); # Emeric Deutsch, Jan 21 2009
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MATHEMATICA
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LinearRecurrence[{9, 72}, {1, 1, 17}, 20] (* Harvey P. Dale, Apr 26 2016 *)
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PROG
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(Magma) I:=[1, 17]; [1] cat [n le 2 select I[n] else 9*(Self(n-1) +8*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 20 2021
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-8*x-64*x^2)/(1-9*x-72*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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