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A015251 Gaussian binomial coefficient [ n,2 ] for q = -3. 4
1, 7, 70, 610, 5551, 49777, 448540, 4035220, 36321901, 326882347, 2941985410, 26477735830, 238300021051, 2144698993717, 19302294530680, 173720640014440, 1563485792415001, 14071372034879887 (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

G. C. Greubel, Table of n, a(n) for n = 2..500

Index entries for linear recurrences with constant coefficients, signature (7,21,-27).

FORMULA

G.f.: x^2/[(1-x)(1+3x)(1-9x)].

a(n) = 10*a(n-1) - 9*a(n-2) + (-1)^n *3^(n-2), n >= 4. - Vincenzo Librandi, Mar 20 2011

a(n) = 7*a(n-1) + 21*a(n-2) - 27*a(n-3), n >= 3. - Vincenzo Librandi, Mar 20 2011

a(n) = (1/96)*(2*(-1)^n*3^n - 3 + 9^n). - R. J. Mathar, Mar 21 2011

MATHEMATICA

Table[QBinomial[n, 2, -3], {n, 2, 25}] (* G. C. Greubel, Jul 30 2016 *)

PROG

(Sage) [gaussian_binomial(n, 2, -3) for n in xrange(2, 18)] # Zerinvary Lajos, May 28 2009

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -27, 21, 7]^(n-2)*[1; 7; 70])[1, 1] \\ Charles R Greathouse IV, Jul 30 2016

CROSSREFS

Sequence in context: A063416 A201065 A043034 * A299870 A196662 A249750

Adjacent sequences:  A015248 A015249 A015250 * A015252 A015253 A015254

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified March 26 20:42 EDT 2019. Contains 321534 sequences. (Running on oeis4.)