A011795 a(n) = floor(C(n,4)/5).
0, 0, 0, 0, 0, 1, 3, 7, 14, 25, 42, 66, 99, 143, 200, 273, 364, 476, 612, 775, 969, 1197, 1463, 1771, 2125, 2530, 2990, 3510, 4095, 4750, 5481, 6293, 7192, 8184, 9275, 10472, 11781, 13209, 14763, 16450, 18278, 20254, 22386, 24682, 27150, 29799, 32637, 35673, 38916, 42375, 46060, 49980, 54145, 58565, 63250, 68211, 73458, 79002, 84854, 91025, 97527, 104371
Offset: 0
References
- J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 147.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- 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 pp. 3, 11, 19.
- Index entries for sequences related to Lyndon words
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1,-4,6,-4,1).
Crossrefs
Programs
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Magma
[Floor(Binomial(n+1,5)/(n+1)): n in [0..70]]; // Vincenzo Librandi Jun 19 2012
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Maple
seq(floor(binomial(n,4)/5), n=0.. 70); # Zerinvary Lajos, Jan 12 2009
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Mathematica
CoefficientList[Series[x^5(1+x^3)/((1-x)^3(1-x^2)(1-x^5)),{x,0,70}],x] (* Vincenzo Librandi, Jun 19 2012 *) CoefficientList[Series[x^4/5 (1/(1-x)^5-1/(1- x^5)),{x,0,70}],x] (* Herbert Kociemba, Oct 16 2016 *) -
PARI
a(n)=binomial(n,4)\5 \\ Charles R Greathouse IV, Oct 07 2015
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SageMath
[binomial(n,4)//5 for n in range(71)] # G. C. Greubel, Oct 20 2024
Formula
G.f.: x^5*(1+x^3)/((1-x)^3*(1-x^2)*(1-x^5)) = x^5*(1-x+x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)).
a(n) = floor(binomial(n+1,5)/(n+1)). - Gary Detlefs, Nov 23 2011
Comments