id:A097325 - OEIS Search Results

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Periodic sequence 0,1,1,1,1,1...

+0
4

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

	OFFSET	`0,1`
	COMMENT	`a(n) is 0 if 6 divides n, 1 otherwise.`
	FORMULA	`G.f.: 1/(1-x) - 1/(1-x^6) = Sum[k>=0, x^k - x^(6k)].` `Recurrence: a(n+6) = a(n), a(0) = 0, a(i) = 1, 1 <= i <= 5.` `a(n) = (1/4) * {3 - (-1)^n - (-1)^[(n+1)/3] - (-1)^[(2n+1)/3]}.` `a(n)={[(1/3)(cos(2nPi/3)+1/2)(1+(-1)^n)]-1}^2 - Paolo P. Lava (ppl(AT)spl.at), Oct 09 2006`
	PROGRAM	`(PARI) a(n) = sign(n%6)`
	CROSSREFS	`Characteristic sequence of A047253. Binary complement of A079979.` `Adjacent sequences: A097322 A097323 A097324 this_sequence A097326 A097327 A097328` `Sequence in context: A143536 A080110 A122895 this_sequence A106549 A075897 A135947`
	KEYWORD	`nonn,easy`
	AUTHOR	`Ralf Stephan, Aug 16 2004`

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Last modified October 13 09:05 EDT 2008. Contains 145008 sequences.

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