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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 range(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 February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)