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A015271 Gaussian binomial coefficient [ n,3 ] for q = -4. 3
1, -51, 3485, -219555, 14107485, -901984419, 57741320029, -3695215419555, 236497451900765, -15135778281070755, 968690748238618461, -61996192875273494691, 3967756584209486471005, -253936417546335462858915 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

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 = 3..200

Index entries for linear recurrences with constant coefficients, signature (-51,884,3264,-4096).

FORMULA

G.f.: x^3/((1-x)*(1+4*x)*(1-16*x)*(1+64*x)). - Bruno Berselli, Oct 29 2012

a(n) = (-1 + 13*2^(4n-6) + (-1)^n*4^(n-2)*(13-2^(4n-2)))/4875. - Bruno Berselli, Oct 29 2012

a(n) = -51*a(n-1)+884*a(n-2)+3264*a(n-3)-4096*a(n-4). - Wesley Ivan Hurt, Sep 04 2022

MATHEMATICA

Table[QBinomial[n, 3, -4], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

PROG

(Sage) [gaussian_binomial(n, 3, -4) for n in range(3, 17)] # Zerinvary Lajos, May 27 2009

CROSSREFS

Sequence in context: A172742 A172821 A172868 * A221116 A099397 A093251

Adjacent sequences:  A015268 A015269 A015270 * A015272 A015273 A015274

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified October 6 04:36 EDT 2022. Contains 357261 sequences. (Running on oeis4.)