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

%I M4717

%S 0,1,10,57,272,885,2226,4725,8912,15417,24970,38401,56640,80717,

%T 111762,151005,199776,259505,331722,418057,520240,640101,779570,

%U 940677,1125552,1336425,1575626,1845585,2148832,2487997,2865810

%N (25*n^4-120*n^3+209*n^2-108*n)/6.

%D 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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harvey P. Dale, <a href="/A006529/b006529.txt">Table of n, a(n) for n = 0..1000</a>

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).

%F 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]

%F G.f.: (-77*x^4-17*x^3-5*x^2-x)/(x-1)^5 [From Harvey P. Dale, Oct 30 2011]

%p A006529:=-z*(1+5*z+17*z**2+77*z**3)/(z-1)**5; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]

%t 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 *)

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_.

%E _Jud McCranie_ noticed this error and gave the correct version of this sequence (A047780).

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Last modified October 21 10:29 EDT 2018. Contains 316414 sequences. (Running on oeis4.)