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A015257
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Gaussian binomial coefficient [ n,2 ] for q=-6.
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3
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1, 31, 1147, 41107, 1480963, 53308003, 1919128099, 69088371619, 2487182817955, 89538572808355, 3223388672928931, 116041991914472611, 4177511710786827427, 150390421577130906787, 5414055176843881927843, 194905986365976733701283
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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 (31,186,-216).
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FORMULA
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G.f.: x^2/((1-x)*(1+6*x)*(1-36*x)).
a(2) = 1, a(3) = 31, a(4) = 1147, a(n) = 31*a(n-1) + 186*a(n-2) - 216*a(n-3). - Vincenzo Librandi, Oct 27 2012
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MATHEMATICA
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Table[QBinomial[n, 2, -6], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 2, -6) for n in xrange(2, 17)] # [From Zerinvary Lajos, May 27 2009]
(MAGMA) I:=[1, 31, 1147]; [n le 3 select I[n] else 31*Self(n-1) + 186*Self(n-2) - 216*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 27 2012
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CROSSREFS
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Sequence in context: A154808 A218285 A138861 * A199234 A123826 A130004
Adjacent sequences: A015254 A015255 A015256 * A015258 A015259 A015260
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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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