A015249 Gaussian binomial coefficient [ n,2 ] for q = -2.

1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575, 244335800775, 977343902151, 3909374210503, 15637499638215

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 (3,6,-8)

Formula

G.f.: x^2/((1-x)*(1+2*x)*(1-4*x)).

a(n) = 5*a(n-1) - 4*a(n-2) + (-1)^n *2^(n-2), n >= 4. - Vincenzo Librandi, Mar 20 2011

a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3), n >= 3. - Vincenzo Librandi, Mar 20 2011

a(n) = (1/18)*(4^n - 2 + (-1)^n*2^n). - R. J. Mathar, Mar 21 2011

Mathematica

Join[{a=1, b=3}, Table[c=2*b+8*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011 *)
Table[QBinomial[n, 2, -2], {n, 2, 25}] (* G. C. Greubel, Jul 30 2016 *)

Prog

(Sage) [gaussian_binomial(n, 2, -2) for n in range(2, 25)] # Zerinvary Lajos, May 28 2009
(PARI) a(n)=(4^n - 2 + (-1)^n*2^n)/18 \\ Charles R Greathouse IV, Jul 30 2016

Crossrefs

Except for initial terms, same as A084152 and A084175.

Sequence in context: A152896 A007973 A261737 * A084152 A084175 A081951

Adjacent sequences: A015246 A015247 A015248 * A015250 A015251 A015252

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved