id:A086928 - OEIS Search Results

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a(n) = 12a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 12, a(n) = (6+sqrt(37))^n + (6-sqrt(37))^n.

+0
2

2, 12, 146, 1764, 21314, 257532, 3111698, 37597908, 454286594, 5489037036, 66322731026, 801361809348, 9682664443202, 116993335127772, 1413602685976466, 17080225566845364, 206376309488120834 (list; graph; listen)

	OFFSET	`0,1`
	COMMENT	`a(n+1)/a(n) converges to (6+sqrt(37)) =12.0827625... a(0)/a(1)=2/12; a(1)/a(2)=12/146; a(2)/a(3)=146/1764; a(3)/a(4)=1764/21314; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.0827625... = 1/(6+sqrt(37)) = (sqrt(37)-6).`
	LINKS	`Tanya Khovanova, Recursive Sequences` `Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)`
	FORMULA	`G.f.: (2-12x)/(1-12x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2008]`
	EXAMPLE	`a(4) = 21314 = 12a(3) + a(2) = 12*1764 + 146 = (6+sqrt(37))^4 + (6-sqrt(37))^4 =` `21313.999953 + 0.000047 = 21314`
	CROSSREFS	`Cf. A001927.` `Sequence in context: A052742 A035049 A010790 this_sequence A001927 A105558 A126777` `Adjacent sequences: A086925 A086926 A086927 this_sequence A086929 A086930 A086931`
	KEYWORD	`easy,nonn`
	AUTHOR	`Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003`

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Last modified December 6 11:04 EST 2009. Contains 170427 sequences.

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