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A014990
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a(n) = (1 - (-8)^n)/9.
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10
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1, -7, 57, -455, 3641, -29127, 233017, -1864135, 14913081, -119304647, 954437177, -7635497415, 61083979321, -488671834567, 3909374676537, -31274997412295, 250199979298361, -2001599834386887, 16012798675095097
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OFFSET
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1,2
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COMMENTS
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q-integers for q=-8.
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LINKS
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FORMULA
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a(n) = a(n-1) + q^{(n-1)} = {(q^n - 1) / (q - 1)}
a(1)=1, a(2)=-7, a(n) = -7*a(n-1) + 8*a(n-2) for n > 2.
G.f.: x/(1 + 7*x - 8*x^2). (End)
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MAPLE
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a:=n->sum ((-8)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008
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MATHEMATICA
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QBinomial[Range[20], 1, -8] (* or *) LinearRecurrence[{-7, 8}, {1, -7}, 20] (* Harvey P. Dale, Dec 19 2011 *)
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PROG
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(Sage) [gaussian_binomial(n, 1, -8) for n in range(1, 20)] # Zerinvary Lajos, May 28 2009
(Magma) I:=[1, -7]; [n le 2 select I[n] else -7*Self(n-1) +8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012
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CROSSREFS
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Cf. A015565, A077925, A014983, A014985, A014986, A014987, A014989, A014991, A014992, A014993, A014994.
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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