A104162 - OEIS

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A104162

Indicator sequence for the Fibonacci numbers.

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; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`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 * A145679 A007273 A016319` `Adjacent sequences: A104159 A104160 A104161 * A104163 A104164 A104165`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Apr 01 2005`

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Last modified February 14 10:43 EST 2012. Contains 205614 sequences.