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A015251
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Gaussian binomial coefficient [ n,2 ] for q = -3.
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4
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1, 7, 70, 610, 5551, 49777, 448540, 4035220, 36321901, 326882347, 2941985410, 26477735830, 238300021051, 2144698993717, 19302294530680, 173720640014440, 1563485792415001, 14071372034879887
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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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FORMULA
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G.f.: x^2/[(1-x)(1+3x)(1-9x)].
a(n) = 10*a(n-1) - 9*a(n-2) + (-1)^n *3^(n-2), n >= 4. - Vincenzo Librandi, Mar 20 2011
a(n) = (1/96)*(2*(-1)^n*3^n - 3 + 9^n). - R. J. Mathar, Mar 21 2011
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MATHEMATICA
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Table[QBinomial[n, 2, -3], {n, 2, 25}] (* G. C. Greubel, Jul 30 2016 *)
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PROG
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(Sage) [gaussian_binomial(n, 2, -3) for n in range(2, 18)] # Zerinvary Lajos, May 28 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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