A015258 Gaussian binomial coefficient [ n,2 ] for q = -7.

1, 43, 2150, 105050, 5149551, 252313293, 12363454300, 605808540100, 29684623509101, 1454546516636543, 71272779562356450, 3492366196825305150, 171125943656551078651, 8385171239086224969793, 410873390715818468708600, 20132796145070950850400200

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

Vincenzo Librandi, Table of n, a(n) for n = 2..200

Index entries for linear recurrences with constant coefficients, signature (43,301,-343).

Formula

G.f.: x^2/((1-x)*(1+7x)*(1-49x)).

a(n) = (6*(-7)^n - 7 +49^n)/2688. - R. J. Mathar, May 25 2011

a(n) = 43*a(n-1) + 301*a(n-2) - 343*a(n-3), n >= 5. - Harvey P. Dale, May 25 2011

Mathematica

CoefficientList[Series[1/((1-x)(1+7x)(1-49x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{43, 301, -343}, {1, 43, 2150}, 20] (* Harvey P. Dale, May 25 2011 *)
Table[QBinomial[n, 2, -7], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *)

Prog

(Sage) [gaussian_binomial(n, 2, -7) for n in range(2, 16)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 43, 2150]; [n le 3 select I[n] else 43*Self(n-1) + 301*Self(n-2) - 343*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 27 2012

Crossrefs

Sequence in context: A267532 A335207 A076572 * A130014 A246535 A265234

Adjacent sequences: A015255 A015256 A015257 * A015259 A015260 A015261

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved