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A015271
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Gaussian binomial coefficient [ n,3 ] for q = -4.
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3
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1, -51, 3485, -219555, 14107485, -901984419, 57741320029, -3695215419555, 236497451900765, -15135778281070755, 968690748238618461, -61996192875273494691, 3967756584209486471005, -253936417546335462858915
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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3,2
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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^3/((1-x)*(1+4*x)*(1-16*x)*(1+64*x)). - Bruno Berselli, Oct 29 2012
a(n) = (-1 + 13*2^(4n-6) + (-1)^n*4^(n-2)*(13-2^(4n-2)))/4875. - Bruno Berselli, Oct 29 2012
a(n) = -51*a(n-1)+884*a(n-2)+3264*a(n-3)-4096*a(n-4). - Wesley Ivan Hurt, Sep 04 2022
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 3, -4) for n in range(3, 17)] # Zerinvary Lajos, May 27 2009
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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