id:A106729 - OEIS Search Results

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Sum of two consecutive squares of Lucas numbers (A001254).

+0
4

5, 10, 25, 65, 170, 445, 1165, 3050, 7985, 20905, 54730, 143285, 375125, 982090, 2571145, 6731345, 17622890, 46137325, 120789085, 316229930 (list; graph; listen)

	OFFSET	`0,1`
	LINKS	`Index entries for sequences related to linear recurrences with constant coefficients` `Tanya Khovanova, Recursive Sequences`
	FORMULA	`a(n) = L(n)^2 + L(n+1)^2 = 5{F(n)^2 + F(n+1)^2} = 5A001519(n).` `a(n)=3a(n-1)-a(n-2) - T. D. Noe (noe(AT)sspectra.com), Dec 11 2006` `G.f.: 5(1-x)/(1-3x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]` `a(n)=(5/2)[(3/2)+(1/2)sqrt(5)]^n+(1/2)[(3/2)+(1/2)sqrt(5)]^nsqrt(5)-(1/2)[(3/2)-(1/2)sqrt(5)]^n sqrt(5)+(5/2)[(3/2)-(1/2)sqrt(5)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]`
	CROSSREFS	`Cf. A000204.` `Sequence in context: A045620 A025625 A112024 this_sequence A038252 A083010 A166388` `Adjacent sequences: A106726 A106727 A106728 this_sequence A106730 A106731 A106732`
	KEYWORD	`nonn`
	AUTHOR	`Lekraj Beedassy (blekraj(AT)yahoo.com), May 14 2005`
	EXTENSIONS	`Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 11 2006`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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