A080924 - OEIS

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A080924

Jacobsthal gap sequence.

0, 1, 3, 1, 15, 1, 63, 1, 255, 1, 1023, 1, 4095, 1, 16383, 1, 65535, 1, 262143, 1, 1048575, 1, 4194303, 1, 16777215, 1, 67108863, 1, 268435455, 1, 1073741823, 1, 4294967295, 1, 17179869183, 1, 68719476735, 1, 274877906943, 1, 1099511627775, 1 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`Inverse binomial transform of A080925` `From Peter Bala, Dec 26 2012: (Start)` `Let F(x) = product {n >= 0} (1 - x^(3n+1))/(1 - x^(3n+2)). This sequence is the simple continued fraction expansion of the real number F(1/4) = 0.79761 68651 30459 16010 ... = 1/(1 + 1/(3 + 1/(1 + 1/(15 + 1/(1 + 1/(63 + 1/(1 + 1/(255 + ...)))))))). See A111317.` `(End)`
	LINKS	`Table of n, a(n) for n=0..41.`
	FORMULA	`a(2n)=3A001045(2n)=3A002450(n)=4^n-1 a(2n+1)=1` `a(n)=(2^n-2(-1)^n+(-2)^n)/2; G.f.: x(1+4x)/((1+x)(1+2x)(1-2x)); E.g.f. : (exp(2x)-2exp(-x)+exp(-2x))/2. - Paul Barry, May 16 2003`
	CROSSREFS	`Cf. A001045, A002450, A080926, A080927.` `Cf. A111317.` `Sequence in context: A214073 A141459 A176727 * A128042 A108083 A163239` `Adjacent sequences: A080921 A080922 A080923 * A080925 A080926 A080927`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry, Feb 26 2003`
	STATUS	`approved`

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Last modified May 20 02:57 EDT 2013. Contains 225446 sequences.