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A011796
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Number of irreducible alternating Euler sums of depth 6 and weight 6+2n.
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2
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1, 3, 9, 20, 42, 75, 132, 212, 333, 497, 728, 1026, 1428, 1932, 2583, 3384, 4389, 5598, 7084, 8844, 10962, 13442, 16380, 19776, 23751, 28301, 33561, 39536, 46376, 54081, 62832, 72624, 83655, 95931, 109668, 124866, 141778, 160398
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n-6)=number of aperiodic necklaces (Lyndon words) with 6 black beads and n-6 white beads.
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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.
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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
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FORMULA
| G.f.: (1+x+2x^2+2x^3+3x^4+2x^6+x^7)/((1-x)^2(1-x^2)^2(1-x^3)(1-x^6)).
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MAPLE
| (Maple) a := n -> (Matrix([[42, 20, 9, 3, 1, 0$7, -1, -4, -9]]). Matrix(15, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -3, -1, 1, 4, -3, -3, 4, 1, -1, -3, 1, 2, -1][i] else 0 fi)^(n-5))[1, 1] ; seq (a(n), n=1..38); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
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CROSSREFS
| Cf. A000031, A001037, A051168. a(n) = T(n, 6), array T as in A051168.
Sequence in context: A192951 A027114 A145070 * A164680 A176163 A203861
Adjacent sequences: A011793 A011794 A011795 * A011797 A011798 A011799
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), David Broadhurst (D.Broadhurst(AT)open.ac.uk)
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