A006529 (25*n^4-120*n^3+209*n^2-108*n)/6. (Formerly M4717)

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

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

Sequence in context: A055251 A038733 A004142 * A337001 A246754 A024133

Adjacent sequences: A006526 A006527 A006528 * A006530 A006531 A006532

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

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

Status

approved