id:A065622 - OEIS Search Results

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Numerator of 1 - (3/4)^n - frac[(3/2)^n)], where frac[x]=x-floor[x].

+0
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0, -1, 3, 13, 159, 173, 1767, 12789, 17759, 126237, 292183, 1930245, 3724303, 23940141, 14206087, 99585429, 640559295, 12562430525, 7042526903, 43417422885, 813747135599, 494896655693, 3000760993767, 18098709141429, 249612172740383 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`The presumption that the fraction is positive for n>1 underlies the presumed solution to Waring's problem.`
	LINKS	`Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.`
	FORMULA	`a(n) = 4^n(1+floor[(3/2)^n])-3^n-6^n = A005061(n)-A002380(n)A000079(n) = A000302(n)*(1+A002379(n))-A000244(n)-A000400(n).`
	EXAMPLE	`a(3) = 13 since 1-(3/4)^3-frac[(3/2)^3)] = 1-27/64-frac[27/8] = 1-27/64-3/8 = (64-27-24)/64 = 13/64.`
	CROSSREFS	`Denominator is A000302. Cf. A002804.` `Sequence in context: A001150 A108554 A014376 this_sequence A114317 A081299 A117808` `Adjacent sequences: A065619 A065620 A065621 this_sequence A065623 A065624 A065625`
	KEYWORD	`frac,sign`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Dec 03 2001`

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Last modified July 4 18:25 EDT 2008. Contains 140886 sequences.

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