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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (31,-155,125)
FORMULA
G.f.: x^2/[(1-x)(1-5x)(1-25x)].
a(n) = 6*a(n-1) - 5*a(n-2) + 25^(n-2), n>=4. - Vincenzo Librandi, Mar 20 2011
a(n) = 30*a(n-1) - 125*a(n-2) + 1, n>=3. - Vincenzo Librandi, Mar 20 2011
a(n) = -5^(n-1)/16 + 25^n/480 + 1/96. - R. J. Mathar, Mar 21 2011
MAPLE
A006111:=-1/(z-1)/(25*z-1)/(5*z-1); # [Simon Plouffe in his 1992 dissertation with offset 0]
MATHEMATICA
Transpose[NestList[Flatten[{Last[#], 30Last[#]- 125First[#]+1}]&, {1, 31}, 20]] [[1]] (* Harvey P. Dale, Mar 26 2011 *)
LinearRecurrence[{31, -155, 125}, {1, 31, 806}, 10] (* T. D. Noe, Mar 26 2011 *)
PROG
(Sage) [gaussian_binomial(n, 2, 5) for n in range(2, 16)] # Zerinvary Lajos, May 28 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Mar 26 2011
STATUS
approved