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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 (list; graph; refs; listen; history; text; internal format)
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
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

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Last modified March 29 03:39 EDT 2024. Contains 371264 sequences. (Running on oeis4.)