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
KEYWORD
nonn
AUTHOR
STATUS
approved