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A014991
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(1 - (-9)^n)/10.
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7
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1, -8, 73, -656, 5905, -53144, 478297, -4304672, 38742049, -348678440, 3138105961, -28242953648, 254186582833, -2287679245496, 20589113209465, -185302018885184, 1667718169966657, -15009463529699912
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OFFSET
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1,2
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COMMENTS
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q-integers for q=-9.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-8,9).
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FORMULA
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a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
a(0)=1, a(1)=-8, a(n) = -8*a(n-1)+9*a(n-2) [Harvey P. Dale, Aug 08 2011]
G.f.: x/((1 - x)*(1 + 9*x)). - Vincenzo Librandi, Oct 22 2012
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MAPLE
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a:=n->sum ((-9)^j, j=0..n): seq(a(n), n=0..25); # [From Zerinvary Lajos, Dec 16 2008]
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MATHEMATICA
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((-9)^Range[30]-1)/-10 (* or *) LinearRecurrence[{-8, 9}, {1, -8}, 30] (* Harvey P. Dale, Aug 08 2011 *)
CoefficientList[Series[1/((1 - x)*(1 + 9*x)), {x, 0, 30}], x]; (* Vincenzo Librandi, Oct 22 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 1, -9) for n in xrange(1, 19)] # [From Zerinvary Lajos, May 28 2009]
(MAGMA) I:=[1, -8]; [n le 2 select I[n] else -8*Self(n-1)+9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012
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CROSSREFS
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Cf. A077925, A014983, A014985-A014987, A014989-A014994. [From Zerinvary Lajos, Dec 16 2008]
Sequence in context: A096873 A241630 A153482 * A015577 A082764 A254150
Adjacent sequences: A014988 A014989 A014990 * A014992 A014993 A014994
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KEYWORD
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sign,easy
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AUTHOR
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Olivier Gérard
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EXTENSIONS
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Better name from Ralf Stephan, Jul 14 2013
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STATUS
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approved
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