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A015257
Gaussian binomial coefficient [ n,2 ] for q = -6.
3
1, 31, 1147, 41107, 1480963, 53308003, 1919128099, 69088371619, 2487182817955, 89538572808355, 3223388672928931, 116041991914472611, 4177511710786827427, 150390421577130906787, 5414055176843881927843, 194905986365976733701283
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.
FORMULA
G.f.: x^2/((1-x)*(1+6*x)*(1-36*x)).
a(2) = 1, a(3) = 31, a(4) = 1147, a(n) = 31*a(n-1) + 186*a(n-2) - 216*a(n-3). - Vincenzo Librandi, Oct 27 2012
MATHEMATICA
Table[QBinomial[n, 2, -6], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *)
PROG
(Sage) [gaussian_binomial(n, 2, -6) for n in range(2, 17)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 31, 1147]; [n le 3 select I[n] else 31*Self(n-1) + 186*Self(n-2) - 216*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 27 2012
CROSSREFS
Sequence in context: A307588 A218285 A138861 * A199234 A123826 A130004
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved