OFFSET
0,3
REFERENCES
M. Gardner, New Mathematical Diversions from Scientific American. Simon and Schuster, NY, 1966, p. 246, gives this as the number of ways to color faces of a cube using at most n colors, but the formula is incorrect (it was corrected in the second printing) - see A047780.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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 (5, -10, 10, -5, 1).
FORMULA
a(0)=0, a(1)=1, a(2)=10, a(3)=57, a(4)=272, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Oct 30 2011]
G.f.: (-77*x^4-17*x^3-5*x^2-x)/(x-1)^5. - Harvey P. Dale, Oct 30 2011
MAPLE
A006529:=-z*(1+5*z+17*z**2+77*z**3)/(z-1)**5; [Conjectured by Simon Plouffe in his 1992 dissertation.]
MATHEMATICA
Table[(25n^4-120n^3+209n^2-108n)/6, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {0, 1, 10, 57, 272}, 40] (* Harvey P. Dale, Oct 30 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Jud McCranie noticed this error and gave the correct version of this sequence (A047780).
STATUS
approved