OFFSET
0,3
COMMENTS
The o.g.f. of this sequence enabled the analysis of A162008, A162009 and A162010. - Johannes W. Meijer, Jun 27 2009
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
A. Fransen, Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.
C. L. Mallows, Letter to N. J. A. Sloane, May 16 1973
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
G. Viennot, Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi, J. Combin. Theory, A 29 (1980), 121-133.
Index entries for linear recurrences with constant coefficients, signature (11,-19,9).
FORMULA
G.f. -x*(1+3*x)/(9*x-1)/(x-1)^2; - Simon Plouffe in his 1992 dissertation.
a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3). - Johannes W. Meijer, Jun 27 2009
a(n) = a(n-1) + (3^(2*n-1) - 1)/2. - Lechoslaw Ratajczak, Jul 06 2016
E.g.f.: (-3 - 8*x + 3*exp(8*x))*exp(x)/16. - Ilya Gutkovskiy, Jul 07 2016
MATHEMATICA
LinearRecurrence[{11, -19, 9}, {0, 1, 14}, 100] (* G. C. Greubel, Jul 06 2016 *)
Table[(3^(2 n + 1) - 8 n - 3)/16, {n, 0, 24}] (* Michael De Vlieger, Jul 08 2016 *)
CROSSREFS
From Johannes W. Meijer, Jun 27 2009: (Start)
Equals the second right hand column of triangle A162005 divided by 2.
(End)
KEYWORD
nonn,easy
AUTHOR
STATUS
approved