OFFSET
12,2
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 = 12..180
FORMULA
a(n) = Product_{i=1..12} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012
MATHEMATICA
QBinomial[Range[12, 20], 12, -3] (* Harvey P. Dale, Dec 18 2011 *)
Table[QBinomial[n, 12, -3], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
PROG
(Sage) [gaussian_binomial(n, 12, -3) for n in range(12, 20)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 06 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved