A117576 - OEIS

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A117576

Expansion of (1-x^3)/((1-x^2)(1+2x^2)).

1, 0, -1, -1, 3, 1, -5, -3, 11, 5, -21, -11, 43, 21, -85, -43, 171, 85, -341, -171, 683, 341, -1365, -683, 2731, 1365, -5461, -2731, 10923, 5461, -21845, -10923, 43691, 21845, -87381, -43691, 174763, 87381, -349525, -174763, 699051 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,5`
	COMMENTS	`A signed pair-reversal of the Jacobsthal numbers A001045. Diagonal sums of A116949.`
	FORMULA	`G.f.: (1+x+x^2)/(1+x+2x^2+2x^3); a(n)=-a(n-1)-2a(n-2)-2a(n-3); a(n)=2^(n/2)(2cos(pin/2)/3+sqrt(2)sin(pin/2)/6)+(-1)^n/3;`
	CROSSREFS	`Cf. A112447.` `Sequence in context: A077881 A129095 A105604 * A112447 A171382 A002323` `Adjacent sequences: A117573 A117574 A117575 * A117577 A117578 A117579`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Mar 29 2006`

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Last modified February 15 20:26 EST 2012. Contains 205852 sequences.