OFFSET
1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10.
F. R. McMorris and T. Zaslavsky, The number of cladistic characters, Math. Biosciences, 54 (1981), 3-10. [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 (10,-35,50,-24).
FORMULA
The terms a(1)-a(18) are given by a(n) = (8/3)*(4^n - 4) - 9*3^n + 11*2^n + 5. - John W. Layman, Jul 20 1999
Formula of Layman matches the proven formula in McMorris and Zaslavsky. - Sean A. Irvine, Apr 12 2016
E.g.f.: (1/3)*(-17*exp(x) + 66*exp(2*x) - 81*exp(3*x) + 32*exp(4*x)). - Ilya Gutkovskiy, Apr 12 2016
G.f.: 2*x^3*(5 + 12*x)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Andrew Howroyd, Mar 28 2025
MAPLE
A005174:=2*z**2*(5+12*z)/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); # conjectured by Simon Plouffe in his 1992 dissertation
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name clarified by Andrew Howroyd, Mar 28 2025
STATUS
approved
