OFFSET
0,2
REFERENCES
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 112.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 35.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)
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
Index entries for linear recurrences with constant coefficients, signature (14,-49,36).
FORMULA
a(n) = 1/24 - 4^(n+2)/15 + 9^(n+2)/40. - Antonio Alberto Olivares, Feb 03 2010
a(n) = 13*a(n-1) - 36*a(n-2) + 1, n >= 2. - Vincenzo Librandi, Mar 23 2011
MAPLE
a:=n->sum((9^(n-j)-4^(n-j))/5, j=0..n): seq(a(n), n=1..30); # Zerinvary Lajos, Jan 15 2007
A002451:=-1/(z-1)/(4*z-1)/(9*z-1); # Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[1/((1-x)(1-4x)(1-9x)), {x, 0, 30}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
PROG
(PARI) Vec(1/((1-x)*(1-4*x)*(1-9*x))+O(x^30)) \\ Charles R Greathouse IV, Sep 23 2012
(GAP) List([0..30], n->1/24-4^(n+2)/15+9^(n+2)/40); # Muniru A Asiru, Dec 18 2018
(Magma) [(10 - 4^(n+4) +6*9^(n+2))/240: n in [0..30]]; // G. C. Greubel, Jul 04 2019
(Sage) [(10 - 4^(n+4) +6*9^(n+2))/240 for n in (0..30)] # G. C. Greubel, Jul 04 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved