|
Search: id:A031164
|
|
|
| A031164 |
|
Irreducible Euler sums of weight 8 and depth 10+2n. |
|
+0
3
|
|
| 1, 4, 15, 40, 99, 212, 429, 800, 1430, 2424, 3978, 6288, 9690, 14520, 21318, 30624, 43263, 60060, 82225, 110968, 148005, 195052, 254475, 328640, 420732, 533936, 672452, 840480, 1043460, 1286832, 1577532, 1922496, 2330445
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n-9)=number of aperiodic necklaces (Lyndon words) with 8 black beads and n-8 white beads.
|
|
LINKS
|
D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory
Index entries for sequences related to Lyndon words
|
|
FORMULA
|
G.f.: (1+x^2)/((1-x)*(1-x^2))^4
a(n)=[C(n+8,7)-(n%2)*C((n+7)/2,3)]/8, where C = binomial, n%2 = parity of n (=1 if odd, 0 else). [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 02 2009]
|
|
PROGRAM
|
(PARI) A031164(n)=(binomial(n+8, 7)-if(n%2, binomial(n\2+4, 3)))>>3 [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 02 2009]
|
|
CROSSREFS
|
Cf. A000031, A001037, A051168.
Cf. A032094. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 02 2009]
Sequence in context: A053698 A162867 A059140 this_sequence A116600 A074033 A093920
Adjacent sequences: A031161 A031162 A031163 this_sequence A031165 A031166 A031167
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
David Broadhurst (D.Broadhurst(AT)open.ac.uk)
|
|
|
Search completed in 0.002 seconds
|
