A015331 Gaussian binomial coefficient [ n,6 ] for q = -8.

1, 233017, 62053592185, 16235267484138105, 4257017266254230145657, 1115917479276007905665796729, 292532187604809092430760283523705, 76685521221108550544352295253436844665

Offset: 6

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• easy

References

• 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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 6..190
• Ji Young Choi, A Generalization of Collatz Functions and Jacobsthal Numbers, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.

Programs

Mathematica

QBinomial[Range[6,15],6,-8] (* Harvey P. Dale, Nov 25 2011 *)
Table[QBinomial[n, 6, -8], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-8) for n in range(6,14)] # Zerinvary Lajos, May 27 2009

Formula

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