id:A112280 - OEIS Search Results

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Coefficients, read modulo 9, of the cube of q-series (q;q)_oo.

+0
3

1, 6, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`The cube-root of g.f. A(x) is an integer series (A112281).`
	FORMULA	`G.f.: A(x) = Sum_{n>=0} A112282(n) * x^(n(n+1)/2) where A112282(n) = (-1)^n(2*n+1) (mod 9).`
	EXAMPLE	`A(x) = 1 + 6x + 5x^3 + 2x^6 + 0x^10 + 7x^15 + 4x^21 +... = (1 - 3x + 5x^3 - 7x^6 + 9x^10 - 11x^15 +...) (mod 9).` `A(x)^(1/3) = 1 + 2x - 4x^2 + 15x^3 - 60x^4 + 268x^5 -+...` `Notation: q-series (q;q)_oo = Product_{n>=1} (1-q^n) = 1 + Sum_{n>=1} (-1)^n[q^(n(3n-1)/2) + q^(n(3*n+1)/2)].`
	PROGRAM	`(PARI) {a(n)=polcoeff(sum(k=0, sqrtint(2n+1), (((-1)^k(2k+1))%9)x^(k(k+1)/2)+xO(x^n)), n)}`
	CROSSREFS	`Cf. A112281 (A(x)^(1/3)), A112282 (nonzero terms), A111983 (variant).` `Sequence in context: A100120 A132709 A113024 this_sequence A021627 A079540 A011492` `Adjacent sequences: A112277 A112278 A112279 this_sequence A112281 A112282 A112283`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Sep 01 2005`

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Last modified December 8 08:31 EST 2009. Contains 170430 sequences.

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