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A015255
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Gaussian binomial coefficient [ n,2 ] for q=-5.
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3
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1, 21, 546, 13546, 339171, 8476671, 211929796, 5298179796, 132454820421, 3311368882921, 82784230211046, 2069605714586046, 51740143068101671, 1293503575685289171, 32337589397218492296, 808439734905030992296
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OFFSET
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2,2
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REFERENCES
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J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p, 99.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 2..200
Index entries for linear recurrences with constant coefficients, signature (21,105,-125).
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FORMULA
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G.f.: x^2/((1-x)*(1+5*x)*(1-25*x)).
a(0)=1, a(1)=21, a(2)=546, a(n)=21*a(n-1)+105*a(n-2)-125*a(n-3). - Harvey P. Dale, Jun 24 2011
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MATHEMATICA
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Table[QBinomial[n, 2, -5], {n, 2, 22}] (* or *) LinearRecurrence[ {21, 105, -125}, {1, 21, 546}, 21] (* Harvey P. Dale, Jun 24 2011 *)
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PROG
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(Sage) [gaussian_binomial(n, 2, -5) for n in xrange(2, 18)] # [From Zerinvary Lajos, May 27 2009]
(MAGMA) I:=[1, 21, 546]; [n le 3 select I[n] else 21*Self(n-1) + 105*Self(n-2) - 125*Self(n-3): n in [1..30]] // Vincenzo Librandi, Oct 27 2012
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CROSSREFS
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Sequence in context: A095655 A221766 A080483 * A034789 A194022 A183730
Adjacent sequences: A015252 A015253 A015254 * A015256 A015257 A015258
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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