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A015276 Gaussian binomial coefficient [ n,3 ] for q = -8. 2
1, -455, 236665, -120935815, 61934287481, -31709385606535, 16235267484138105, -8312452980450674055, 4255976180162154314361, -2179059787976052939572615, 1115678612484825190455949945, -571227449525600988055816521095 (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 for linear recurrences with constant coefficients, signature (-455,29640,232960,-262144).

FORMULA

G.f.: x^3/((1-x)*(1+8*x)*(1-64*x)*(1+512*x)). - Bruno Berselli, Oct 30 2012

a(n) = (-1 + 57*8^(2n-3) + (-1)^n*8^(n-2)*(57-8^(2n-1)))/290871. - Bruno Berselli, Oct 30 2012

a(n) = Product_{i=1..3} ((-8)^(n-i+1)-1)/((-8)^i-1) (by definition). - Vincenzo Librandi, Aug 02 2016

MATHEMATICA

Table[QBinomial[n, 3, -8], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

PROG

(Sage) [gaussian_binomial(n, 3, -8) for n in xrange(3, 15)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=3; q:=-8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

CROSSREFS

Sequence in context: A251337 A282232 A061544 * A145528 A203058 A116331

Adjacent sequences:  A015273 A015274 A015275 * A015277 A015278 A015279

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)