login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A015251 Gaussian binomial coefficient [ n,2 ] for q = -3. 4
1, 7, 70, 610, 5551, 49777, 448540, 4035220, 36321901, 326882347, 2941985410, 26477735830, 238300021051, 2144698993717, 19302294530680, 173720640014440, 1563485792415001, 14071372034879887 (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
FORMULA
G.f.: x^2/[(1-x)(1+3x)(1-9x)].
a(n) = 10*a(n-1) - 9*a(n-2) + (-1)^n *3^(n-2), n >= 4. - Vincenzo Librandi, Mar 20 2011
a(n) = 7*a(n-1) + 21*a(n-2) - 27*a(n-3), n >= 3. - Vincenzo Librandi, Mar 20 2011
a(n) = (1/96)*(2*(-1)^n*3^n - 3 + 9^n). - R. J. Mathar, Mar 21 2011
MATHEMATICA
Table[QBinomial[n, 2, -3], {n, 2, 25}] (* G. C. Greubel, Jul 30 2016 *)
PROG
(Sage) [gaussian_binomial(n, 2, -3) for n in range(2, 18)] # Zerinvary Lajos, May 28 2009
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -27, 21, 7]^(n-2)*[1; 7; 70])[1, 1] \\ Charles R Greathouse IV, Jul 30 2016
CROSSREFS
Sequence in context: A063416 A201065 A043034 * A299870 A196662 A249750
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 24 13:58 EDT 2024. Contains 371960 sequences. (Running on oeis4.)