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A015260
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Gaussian binomial coefficient [ n,2 ] for q=-9.
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3
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1, 73, 5986, 484210, 39226915, 3177326971, 257363962948, 20846476694116, 1688564650965445, 136773736379522605, 11078672649879436966, 897372484611991440598, 72687171253825493271271, 5887660871557577275727455, 476900530596184348447133320
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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 (73, 657, -729).
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FORMULA
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G.f.: x^2/((1-x)*(1+9*x)*(1-81*x)).
a(2) = 1, a(3) = 73, a(4) = 5986, a(n) = 73*a(n-1) + 657*a(n-2) - 729*a(n-3). - Vincenzo Librandi, Oct 27 2012
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MATHEMATICA
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Table[QBinomial[n, 2, -9], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 2, -9) for n in xrange(2, 15)] # [From Zerinvary Lajos, May 27 2009]
(MAGMA) I:=[1, 73, 5986]; [n le 3 select I[n] else 73*Self(n-1) + 657*Self(n-2) - 729*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 27 2012
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CROSSREFS
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Sequence in context: A093273 A183540 A022242 * A089788 A192765 A177094
Adjacent sequences: A015257 A015258 A015259 * A015261 A015262 A015263
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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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