id:A164357 - OEIS Search Results

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Expansion of (1 - x^2)^5 / ((1 - x)^4 * (1 - x^6)) in powers of x.

+0
1

1, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5, 0, -5, -4, 0, 4, 5 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`Euler transform of length 6 sequence [ 4, -5, 0, 0, 0, 1].` `a(n) = 4b(n) unless n=0 and b(n) is multiplicative with b(2^e) = -5/4 (-1)^e, b(3^e) = 0^e, b(p^e) = 1 if p == 1 (mod 6), b(p^e) = (-1)^e if p == 5 (mod 6).` `a(-n) = -a(n) unless n=0. a(3n) = 0 unless n=0. a(n+6) = a(n) unless n=0 or n=-6.` `G.f.: 1 + (x/2) ( 9 / (1 - x + x^2) - 1 / (1 + x + x^2)).`
	PROGRAM	`(PARI) {a(n) = (n==0) - 1/2 * kronecker(-3, n) + 9/2 * kronecker(9, n) * (-1)^(n\3) }`
	CROSSREFS	`Sequence in context: A021226 A011286 A159567 this_sequence A092487 A132022 A122753` `Adjacent sequences: A164354 A164355 A164356 this_sequence A164358 A164359 A164360`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Aug 13 2009`

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Last modified March 20 09:10 EDT 2010. Contains 173642 sequences.

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