id:A088210 - OEIS Search Results

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Numerators of convergents of the continued fraction with the n+1 partial quotients: [2;2,2,...(n 2's)...,2,n+1], starting with [1], [2;2], [2;2,3], [2;2,2,4], ...

+0
2

1, 5, 17, 53, 157, 449, 1253, 3433, 9273, 24765, 65529, 172061, 448853, 1164409, 3006157, 7728337, 19794545, 50532469, 128621281, 326513669, 826887693, 2089505841, 5269572021, 13265211961, 33336792745, 83648953133, 209591807177 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`Denominators are A088211. Partial sums form A054459. Second differences form A026937.`
	FORMULA	`G.f.: (1+x)(1-x^2)/(1-2*x-x^2)^2.`
	EXAMPLE	`a(3)/A088211(3) = [2;2,2,4] = 53/22.`
	CROSSREFS	`Cf. A088211, A054459, A026937.` `Adjacent sequences: A088207 A088208 A088209 this_sequence A088211 A088212 A088213` `Sequence in context: A090575 A107167 A110318 this_sequence A135344 A027028 A048473`
	KEYWORD	`frac,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Sep 23 2003`

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Last modified May 16 23:01 EDT 2008. Contains 139884 sequences.

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