id:A143064 - OEIS Search Results

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Expansion of a Ramanujan false theta series variation of A089801 in powers of x.

+0
2

1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; listen)

	OFFSET	`0,1`
	REFERENCES	`S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41`
	FORMULA	`a(n) = b(3n + 1) where b(n) is multiplicative and b(p^(2e)) = (-1)^e if p = 5 (mod 6), b(p^(2e)) = +1 if p = 1 (mod 6) and b(p^(2e-1)) = b(2^e) = b(3^e) = 0 if e>0.` `a(4n + 2) = a(4n + 3) = a(8n + 4) = 0.` `G.f.: Sum_{k>=0} (-1)^k x^(3k^2 + 2k) * ( 1 + x^(2*k+1) ).`
	EXAMPLE	`q + q^4 - q^16 - q^25 + q^49 + q^64 - q^100 - q^121 + q^169 + q^196 + ...`
	PROGRAM	`(PARI) {a(n) = if( issquare( 3*n + 1, &n), (-1)^(n \ 3) )}`
	CROSSREFS	`Cf. A143062(n) = a(8*n). Convolution of A010054 with A143065.` `Sequence in context: A012245 A089801 A089802 this_sequence A163811 A163817 A151667` `Adjacent sequences: A143061 A143062 A143063 this_sequence A143065 A143066 A143067`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Jul 21 2008`

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Last modified December 15 00:47 EST 2009. Contains 170825 sequences.

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