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A015271 Gaussian binomial coefficient [ n,3 ] for q = -4. 3

%I

%S 1,-51,3485,-219555,14107485,-901984419,57741320029,-3695215419555,

%T 236497451900765,-15135778281070755,968690748238618461,

%U -61996192875273494691,3967756584209486471005,-253936417546335462858915

%N Gaussian binomial coefficient [ n,3 ] for q = -4.

%D 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.

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

%H Vincenzo Librandi, <a href="/A015271/b015271.txt">Table of n, a(n) for n = 3..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-51,884,3264,-4096).

%F G.f.: x^3/((1-x)*(1+4*x)*(1-16*x)*(1+64*x)). - _Bruno Berselli_, Oct 29 2012

%F a(n) = (-1 + 13*2^(4n-6) + (-1)^n*4^(n-2)*(13-2^(4n-2)))/4875. - _Bruno Berselli_, Oct 29 2012

%t Table[QBinomial[n, 3, -4], {n, 3, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)

%o (Sage) [gaussian_binomial(n,3,-4) for n in range(3,17)] # _Zerinvary Lajos_, May 27 2009

%K sign,easy

%O 3,2

%A _Olivier GĂ©rard_, Dec 11 1999

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Last modified April 6 18:34 EDT 2020. Contains 333286 sequences. (Running on oeis4.)