A015331 - OEIS

%I #29 Dec 07 2019 12:18:18

%S 1,233017,62053592185,16235267484138105,4257017266254230145657,

%T 1115917479276007905665796729,292532187604809092430760283523705,

%U 76685521221108550544352295253436844665

%N Gaussian binomial coefficient [ n,6 ] for q = -8.

%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="/A015331/b015331.txt">Table of n, a(n) for n = 6..190</a>

%H Ji Young Choi, <a href="https://www.emis.de/journals/JIS/VOL21/Choi/choi10.html">A Generalization of Collatz Functions and Jacobsthal Numbers</a>, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.

%F G.f.: x^6/((1-x)*(1+8*x)*(1-64*x)*(1+512*x)*(1-4096*x)*(1+32768*x)*(1-262144*x)). - _Vincenzo Librandi_, Oct 30 2012

%t QBinomial[Range[6,15],6,-8] (* _Harvey P. Dale_, Nov 25 2011 *)

%t Table[QBinomial[n, 6, -8], {n, 6, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)

%o (Sage) [gaussian_binomial(n,6,-8) for n in range(6,14)] # _Zerinvary Lajos_, May 27 2009

%K nonn,easy

%O 6,2

%A _Olivier Gérard_, Dec 11 1999