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A015286 Gaussian binomial coefficient [ n,3 ] for q = -13. 12
1, -2040, 4508570, -9900819720, 21752862899691, -47790911017216080, 104996653267533662740, -230677643550873536294640, 506798783502833908602716981, -1113436927250681654567602842120 (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..200

Index entries related to Gaussian binomial coefficients.

Index entries for linear recurrences with constant coefficients, signature (-2040,346970,4481880,-4826809)

FORMULA

a(n) = Product_{i=1..3} ((-13)^(n-i+1) - 1)/((-13)^i - 1). - M. F. Hasler, Nov 03 2012

G.f.: x^3 / ( (x-1)*(2197*x+1)*(13*x+1)*(169*x-1) ). - R. J. Mathar, Aug 03 2016

EXAMPLE

A015286(7) = 21752862899691 = A015303(7),

A015286(8) = -47790911017216080 = A015321(8),

A015286(9) = 104996653267533662740 = A015337(9). - M. F. Hasler, Nov 03 2012

MATHEMATICA

QBinomial[Range[3, 15], 3, -13] (* Harvey P. Dale, Jun 21 2012 *)

Table[QBinomial[n, 3, -13], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

PROG

(Sage) [gaussian_binomial(n, 3, -13) for n in xrange(3, 13)] # Zerinvary Lajos, May 27 2009

(PARI) A015286(n, r=3, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

(MAGMA) r:=3; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

CROSSREFS

Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), 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

Fourth row (r=3) or column (resp. diagonal) in A015129 (read as square array resp. triangle). - M. F. Hasler, Nov 03 2012

Sequence in context: A258965 A250009 A015158 * A172594 A115553 A068264

Adjacent sequences:  A015283 A015284 A015285 * A015287 A015288 A015289

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified March 26 05:43 EDT 2019. Contains 321481 sequences. (Running on oeis4.)