A015195 Sum of Gaussian binomial coefficients for q=9.

1, 2, 12, 184, 9104, 1225248, 540023488, 652225844096, 2584219514040576, 28081351726592246272, 1001235747932175990213632, 97915621602690773814148184064, 31420034518763282871588038742544384, 27654326463468067495668136467306727743488

Offset

0,2

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..60

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

Formula

a(n) = 2*a(n-1)+(9^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013

a(n) ~ c * 9^(n^2/4), where c = EllipticTheta[3,0,1/9]/QPochhammer[1/9,1/9] = 1.3946866902389... if n is even and c = EllipticTheta[2,0,1/9]/QPochhammer[1/9,1/9] = 1.333574200539... if n is odd. - Vaclav Kotesovec, Aug 21 2013

Mathematica

Total/@Table[QBinomial[n, m, 9], {n, 0, 20}, {m, 0, n}] (* Vincenzo Librandi, Nov 01 2012 *)
Flatten[{1, RecurrenceTable[{a[n]==2*a[n-1]+(9^(n-1)-1)*a[n-2], a[0]==1, a[1]==2}, a, {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 21 2013 *)

Crossrefs

Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122.

Row sums of triangle A022173.

Sequence in context: A006023 A039748 A007764 * A051421 A182162 A258994

Adjacent sequences: A015192 A015193 A015194 * A015196 A015197 A015198

Keyword

nonn

Author

N. J. A. Sloane, Olivier Gérard

Status

approved