id:A105426 - OEIS Search Results

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a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2).

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1, 5, 39, 307, 2417, 19029, 149815, 1179491, 9286113, 73109413, 575589191, 4531604115, 35677243729, 280886345717, 2211413522007, 17410421830339, 137071961120705, 1079165267135301, 8496250175961703, 66890836140558323 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`15*a(n)^2-14 is a square for all n.`
	LINKS	`Index entries for two-way infinite sequences` `Tanya Khovanova, Recursive Sequences` `Index entries for sequences related to linear recurrences with constant coefficients`
	FORMULA	`G.f.: (1-3x)/(1-8x+x^2). a(n)=2A105045(2n+1)-1. a(-n)=2A105045(2n)-1, if n>0.` `a(n)=(1/2)[4-sqrt(15)]^n-(1/30)[4-sqrt(15)]^nsqrt(15)+(1/2)[4+sqrt(15)]^n+(1/30)sqrt(15) [4+sqrt(15)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 08 2008`
	PROGRAM	`(PARI) a(n)=subst(19*poltchebi(n)-poltchebi(n-1), x, 4)/15`
	CROSSREFS	`Cf. a(n) = A001090(n+1) - 3*A001090(n).` `Sequence in context: A053573 A003482 A135849 this_sequence A115187 A129763 A070767` `Adjacent sequences: A105423 A105424 A105425 this_sequence A105427 A105428 A105429`
	KEYWORD	`nonn`
	AUTHOR	`Michael Somos, Apr 10 2005`

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Last modified December 7 23:50 EST 2009. Contains 170430 sequences.

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