A006529 a(n) = (25*n^4-120*n^3+209*n^2-108*n)/6.

0, 1, 10, 57, 272, 885, 2226, 4725, 8912, 15417, 24970, 38401, 56640, 80717, 111762, 151005, 199776, 259505, 331722, 418057, 520240, 640101, 779570, 940677, 1125552, 1336425, 1575626, 1845585, 2148832, 2487997, 2865810, 3285101, 3748800, 4259937, 4821642

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

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).

Programs

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 *)

Formula

From Harvey P. Dale, Oct 30 2011: (Start)

a(n) = 5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5).

G.f.: (-77*x^4-17*x^3-5*x^2-x)/(x-1)^5. (End)

Extensions

Jud McCranie noticed this error and gave the correct version of this sequence (A047780).