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A006550 n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6). 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
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: A351458 A067250 A061005 * A047780 A055251 A038733
KEYWORD
nonn
AUTHOR
EXTENSIONS
Jud McCranie found this error and gave the correct version of this sequence (A047780).
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)