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A015265 Gaussian binomial coefficient [ n,2 ] for q = -13. 12
1, 157, 26690, 4508570, 761974851, 128773405047, 21762709934980, 3677897920745140, 621564749363392901, 105044442632566365137, 17752510805031727164870, 3000174326048697741925710, 507029461102251552321630151, 85687978926280231101185088427 (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

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

Index entries for linear recurrences with constant coefficients, signature (157, 2041, -2197).

FORMULA

G.f.: x^2/((1-x)*(1+13*x)*(1-169*x)). - Ralf Stephan, Apr 01 2004

a(2) = 1, a(3) = 157, a(4) = 26690, a(n) = 157*a(n-1) + 2041*a(n-2) - 2197*a(n-3). - Vincenzo Librandi, Oct 28 2012

a(n) = (1/2352)*( (1 - (-13)^n)*((-13)^(n-1) - 1) ). - M. F. Hasler, Nov 03 2012

MATHEMATICA

Table[QBinomial[n, 2, -13], {n, 2, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

PROG

(Sage) [gaussian_binomial(n, 2, -13) for n in xrange(2, 14)] # Zerinvary Lajos, May 27 2009

(MAGMA) I:=[1, 157, 26690]; [n le 3 select I[n] else 157*Self(n-1)+2041*Self(n-2)-2197*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012

(PARI) A015265(n, q=-13)=(1-q^n)*(q^(n-1)-1)/2352 \\ M. F. Hasler, Nov 03 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n,2] for q=-2,...,-12: A015249, A015251, A015253, A015255, A015257 A015258, A015259, A015260, A015261, A015262, A015264.

Cf. Gaussian binomial coefficients [n,r] for q=-13: A015286 (r=3), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012

Sequence in context: A066823 A213469 A074220 * A260447 A048930 A130864

Adjacent sequences:  A015262 A015263 A015264 * A015266 A015267 A015268

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified March 21 20:35 EDT 2019. Contains 321382 sequences. (Running on oeis4.)