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A015266 Gaussian binomial coefficient [ n,3 ] for q = -2. 4
1, -5, 55, -385, 3311, -25585, 208335, -1652145, 13275471, -105970865, 848699215, -6785865905, 54301841231, -434355079345, 3475079247695, -27799679551665, 222401254176591, -1779194762447025, 14233619183613775 (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..1000

FORMULA

a(n) = (1/81)*(24*4^n - 6*(-2)^n + 64*(-8)^n - 1). - Paolo P. Lava, Jan 13 2009

From Paul Barry, Jul 12 2005: (Start)

G.f.: x^3/((1-2*x-8*x^2)*(1+7*x-8*x^2));

a(n) = -5*a(n-1) + 30*a(n-2) + 40*a(n-3) - 64*a(n-4);

a(n+3) = (-1)^n*J(n)*J(n+1)*J(n+2)/3, where J(n)=A001045(n). (End)

a(n) = T015109(n,3), where T015109 is the triangular array defined by A015109. - M. F. Hasler, Nov 04 2012

MATHEMATICA

Table[QBinomial[n, 2, -2], {n, 3, 25}] (* G. C. Greubel, Jul 31 2016 *)

PROG

(Sage) [gaussian_binomial(n, 3, -2) for n in xrange(3, 22)] # Zerinvary Lajos, May 27 2009

(MAGMA) [(1/81)*(24*4^n-6*(-2)^n+64*(-8)^n-1): n in [0..20]]; // Vincenzo Librandi, Aug 23 2011

CROSSREFS

Diagonal k=3 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Sequence in context: A060558 A014852 A144893 * A138163 A306095 A081300

Adjacent sequences:  A015263 A015264 A015265 * A015267 A015268 A015269

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)