id:A104162 - OEIS Search Results

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Indicator sequence for the Fibonacci numbers.

+0
17

1, 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 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, 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`Without multiplicities, this is A010056.` `The number of nonnegative integer solutions of x^4-10n^2x^2+25*n^4-16=0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007`
	FORMULA	`G.f. : sum{k>=0, x^F(k)}` `a(n)=1+floor(arsinh(sqr(5)n/2)/ln(phi))-ceiling(arcosh(sqr(5)n/2)/ln(phi)), for n>0, where phi=(1+sqr(5))/2. Also true: a(n)=A108852(n)-A108852(n-1)=A130233(n)-A130233(n-1)=1+A130233(n)-A130234(n) for n>0 and a(n)=A130234(n+1)-A130234(n) for n>=0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007`
	EXAMPLE	`a(1)=2 since F(1)=F(2)=1.`
	CROSSREFS	`Cf. A000045.` `Partial sums are in A108852. See also A130233 and A130234.` `Sequence in context: A160381 A089311 A086784 this_sequence A145679 A007273 A016319` `Adjacent sequences: A104159 A104160 A104161 this_sequence A104163 A104164 A104165`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Apr 01 2005`

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Last modified December 11 12:57 EST 2009. Contains 170656 sequences.

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