A086594 - OEIS

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A086594

a(n)=8a(n-1)+a(n-2), starting with a(0)=2 and a(1)=8.

2, 8, 66, 536, 4354, 35368, 287298, 2333752, 18957314, 153992264, 1250895426, 10161155672, 82540140802, 670482282088, 5446398397506, 44241669462136, 359379754094594, 2919279702218888 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,1`
	COMMENTS	`Harmonious sequence, build on the number 8.1231056...` `a(n+1)/a(n) converges to 4+sqrt(17). a(0)/a(1)=1/4; a(1)/a(2)=8/66; a(2)/a(3)=66/536; a(3)/a(4)=536/4354;...etc. Lim a(n)/a(n+1)as n approaches infinity=0.123105625...=1/(4+sqrt(17))=sqrt(17)-4.`
	LINKS	`Index entries for sequences related to linear recurrences with constant coefficients` `Tanya Khovanova, Recursive Sequences` `Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)`
	FORMULA	`a(n)=(4+sqrt(17))^n+(4-sqrt(17))^n.` `O.g.f: 2(-1+4x)/(-1+8*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2007`
	EXAMPLE	`a(4)=4354=8a(3)+a(2)=8*536+66=(4+sqrt(17))^4+(4-sqrt(17))^4=4353.9997703+` `0.0002297=4354.`
	CROSSREFS	`Cf. A003285.` `Sequence in context: A009602 A011836 A100623 * A132219 A202553 A023164` `Adjacent sequences: A086591 A086592 A086593 * A086595 A086596 A086597`
	KEYWORD	`easy,nonn`
	AUTHOR	`Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003`

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Last modified February 16 10:53 EST 2012. Contains 205904 sequences.