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%I #27 Sep 08 2022 08:44:39
%S 1,31,1147,41107,1480963,53308003,1919128099,69088371619,
%T 2487182817955,89538572808355,3223388672928931,116041991914472611,
%U 4177511710786827427,150390421577130906787,5414055176843881927843,194905986365976733701283
%N Gaussian binomial coefficient [ n,2 ] for q = -6.
%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="/A015257/b015257.txt">Table of n, a(n) for n = 2..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (31,186,-216).
%F G.f.: x^2/((1-x)*(1+6*x)*(1-36*x)).
%F a(2) = 1, a(3) = 31, a(4) = 1147, a(n) = 31*a(n-1) + 186*a(n-2) - 216*a(n-3). - _Vincenzo Librandi_, Oct 27 2012
%t Table[QBinomial[n, 2, -6], {n, 2, 20}] (* _Vincenzo Librandi_, Oct 27 2012 *)
%o (Sage) [gaussian_binomial(n,2,-6) for n in range(2,17)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) I:=[1, 31, 1147]; [n le 3 select I[n] else 31*Self(n-1) + 186*Self(n-2) - 216*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Oct 27 2012
%K nonn,easy
%O 2,2
%A _Olivier Gérard_, Dec 11 1999
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