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%I #23 Dec 07 2019 12:18:18
%S 1,7,70,610,5551,49777,448540,4035220,36321901,326882347,2941985410,
%T 26477735830,238300021051,2144698993717,19302294530680,
%U 173720640014440,1563485792415001,14071372034879887
%N Gaussian binomial coefficient [ n,2 ] for q = -3.
%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 G. C. Greubel, <a href="/A015251/b015251.txt">Table of n, a(n) for n = 2..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,21,-27).
%F G.f.: x^2/[(1-x)(1+3x)(1-9x)].
%F a(n) = 10*a(n-1) - 9*a(n-2) + (-1)^n *3^(n-2), n >= 4. - _Vincenzo Librandi_, Mar 20 2011
%F a(n) = 7*a(n-1) + 21*a(n-2) - 27*a(n-3), n >= 3. - _Vincenzo Librandi_, Mar 20 2011
%F a(n) = (1/96)*(2*(-1)^n*3^n - 3 + 9^n). - _R. J. Mathar_, Mar 21 2011
%t Table[QBinomial[n, 2, -3], {n, 2, 25}] (* _G. C. Greubel_, Jul 30 2016 *)
%o (Sage) [gaussian_binomial(n,2,-3) for n in range(2,18)] # _Zerinvary Lajos_, May 28 2009
%o (PARI) a(n)=([0,1,0; 0,0,1; -27,21,7]^(n-2)*[1;7;70])[1,1] \\ _Charles R Greathouse IV_, Jul 30 2016
%K nonn,easy
%O 2,2
%A _Olivier Gérard_, Dec 11 1999
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