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A004004 a(n) = (3^{2n+1} - 8*n - 3)/16.
(Formerly M4943)
11
0, 1, 14, 135, 1228, 11069, 99642, 896803, 8071256, 72641337, 653772070, 5883948671, 52955538084, 476599842805, 4289398585298, 38604587267739, 347441285409712, 3126971568687473 (list; graph; refs; listen; history; text; internal format)
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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 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

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

MAPLE

A004004:=-z*(1+3*z)/(9*z-1)/(z-1)**2; # [Conjectured by Simon Plouffe in his 1992 dissertation.]

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.

Cf. A162008, A162009, A162010, A162011 and A162014 [2*(1+3*z)].

(End)

Sequence in context: A272652 A016801 A244651 * A002753 A155625 A016296

Adjacent sequences:  A004001 A004002 A004003 * A004005 A004006 A004007

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified October 15 19:24 EDT 2018. Contains 316237 sequences. (Running on oeis4.)