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A020999

Conjectured number of irreducible multiple zeta values of depth n and weight 3n (confirmed up to n=7).

+0
2

1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 10, 14, 17, 24, 30, 41, 53, 72, 93, 126, 165, 222, 293, 395, 522, 704, 936, 1259, 1681, 2263, 3027, 4079, 5470, 7371, 9906, 13361, 17980, 24271, 32712, 44182, 59626, 80598, 108879, 147285, 199165 (list; graph; listen)

	OFFSET	`0,9`
	LINKS	`D. J. Broadhurst, Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams`
	FORMULA	`\prod_n (1-x^n)^{a[ n ]} = 1-x-x^4; equivalently, a[ n ] = (1/n) sum_{ d divides n } \mu(n/d) X_d, where X_d = X_{d-1} + X_{d-4}, with X_1 = X_2 = X_3 = 1, X_4 = 5.`
	CROSSREFS	`Cf. A014097.` `Sequence in context: A035577 A002723 A035937 this_sequence A079955 A136417 A130791` `Adjacent sequences: A020996 A020997 A020998 this_sequence A021000 A021001 A021002`
	KEYWORD	`nonn,nice`
	AUTHOR	`David Broadhurst (D.Broadhurst(AT)open.ac.uk)`

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Last modified July 8 18:40 EDT 2008. Contains 141013 sequences.

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