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A004004 a(n) = (3^{2n+1} - 8*n - 3)/16.
(Formerly M4943)
10
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
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
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.
Cf. A162008, A162009, A162010, A162011 and A162014 [2*(1+3*z)].
(End)
Sequence in context: A016801 A323857 A244651 * A002753 A306301 A155625
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)