A015204 Sum of Gaussian binomial coefficients for q=16.

1, 2, 19, 548, 78901, 36070982, 82805758039, 605336231791208, 22229212008282455161, 2599943776445794193452682, 1527585017328101696333407084699, 2858671468933430533899194300073611948, 26873565540839814480301520088779437828129981

Offset: 0

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn

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 = 0..50
• Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Crossrefs

Row sums of triangle A022180.

Programs

Mathematica

Total/@Table[QBinomial[n, m, 16], {n, 0, 20}, {m, 0, n}] (* Vincenzo Librandi, Nov 02 2012 *)

Formula

a(0) = 1, a(1) = 2, a(n) = 2*a(n-1) + a(n-2)*((16^(n-1)) - 1). - Vincenzo Librandi, Nov 02 2012