OFFSET
2,2
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 = 2..200
Index entries for linear recurrences with constant coefficients, signature (111,1221,-1331).
FORMULA
G.f.: x^2/((1-x)*(1+11*x)*(1-121*x)).
a(n) = 111*a(n-1) + 1221*a(n-2) - 1331*a(n-3); a(2)=1, a(3)=111, a(4)=13542. - Vincenzo Librandi, Oct 28 2012
From Elmo R. Oliveira, Aug 09 2026: (Start)
a(n) = (1/1440)*((-11)^n - 1)*(1 - (-11)^(n-1)).
E.g.f.: (exp(121*x) + 10*exp(-11*x) - 11*exp(x))/15840. (End)
MATHEMATICA
Table[QBinomial[n, 2, -11], {n, 2, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(SageMath) [gaussian_binomial(n, 2, -11) for n in range(2, 20)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 111, 13542]; [n le 3 select I[n] else 111*Self(n-1) + 1221*Self(n-2) - 1331*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved