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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

Vincenzo Librandi, Table of n, a(n) for n = 2..200

Index entries for linear recurrences with constant coefficients, signature (31,186,-216).

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

Adjacent sequences:  A015254 A015255 A015256 * A015258 A015259 A015260

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)