A011797 a(n) = floor(C(n,6)/7).
0, 0, 0, 0, 0, 0, 0, 1, 4, 12, 30, 66, 132, 245, 429, 715, 1144, 1768, 2652, 3876, 5537, 7752, 10659, 14421, 19228, 25300, 32890, 42287, 53820, 67860, 84825, 105183, 129456, 158224, 192129, 231880, 278256
Offset: 0
Links
- David J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, arXiv:hep-th/9604128, 1996.
- David Broadhurst and Xavier Roulleau, Number of partitions of modular integers, arXiv:2502.19523 [math.NT], 2025. See p. 19.
- Index entries for sequences related to Lyndon words
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).
Crossrefs
Programs
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Mathematica
CoefficientList[Series[x^6/7 (1/(1-x)^7-1/(1- x^7)),{x,0,40}],x]; (* Herbert Kociemba, Oct 16 2016 *) -
PARI
a(n) = binomial(n, 6)\7; \\ Michel Marcus, Oct 16 2016
Formula
G.f.: (1+x^3)^2/((1-x)^4(1-x^2)^2(1-x^7))*x^7.
a(n) = floor(binomial(n+1,7)/(n+1)). [Gary Detlefs, Nov 23 2011]
G.f.: (x^6/7)*(1/(1-x)^7-1/(1- x^7)). - Herbert Kociemba, Oct 16 2016
Comments