A006550 n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).

0, 1, 10, 57, 234, 770, 2136, 5180, 11292, 22599, 42190, 74371, 124950, 201552, 313964, 474510, 698456, 1004445, 1414962, 1956829, 2661730, 3566766, 4715040, 6156272, 7947444, 10153475, 12847926, 16113735, 20043982, 24742684, 30325620

Offset

1,3

References

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 254, gives this as number of ways to color faces of a cube using at most n colors, but the formula is incorrect - see A047780.

Links

Table of n, a(n) for n=1..31.

V. Meally, Letter to N. J. A. Sloane, N.D.

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 (7, -21, 35, -35, 21, -7, 1).

Maple

A006550:=(-1-3*z-8*z**2-10*z**3-14*z**4+6*z**5)/(z-1)**7; # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

Table[n+8Binomial[n, 2]+30Binomial[n, 3]+62Binomial[n, 4]+75Binomial[n, 5]+ 30Binomial[n, 6], {n, 0, 40}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 10, 57, 234, 770, 2136}, 40] (* Harvey P. Dale, Apr 24 2011 *)

Crossrefs

Sequence in context: A378894 A067250 A061005 * A047780 A055251 A038733

Adjacent sequences: A006547 A006548 A006549 * A006551 A006552 A006553

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved