A015453 - OEIS

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A015453

Generalized Fibonacci numbers.

1, 1, 8, 57, 407, 2906, 20749, 148149, 1057792, 7552693, 53926643, 385039194, 2749201001, 19629446201, 140155324408, 1000716717057, 7145172343807, 51016923123706, 364263634209749, 2600862362591949, 18570300172353392 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	LINKS	`Index entries for sequences related to linear recurrences with constant coefficients` `Tanya Khovanova, Recursive Sequences`
	FORMULA	`a(n) = 7 a(n-1) + a(n-2).` `a(n)=Sum_{k, 0<=k<=n}6^kA055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006` `a(n)=(5/106)sqrt(53)[7/2-(1/2)sqrt(53)]^n+(1/2)[7/2+(1/2)sqrt(53)]^n+(1/2)[7/2-(1/2) sqrt(53)]^n-(5/106)[7/2+(1/2)sqrt(53)]^nsqrt(53), with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2008` `G.f.: (1-6x)/(1-7*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]`
	CROSSREFS	`Sequence in context: A023000 A097114 A022038 * A181246 A199555 A002402` `Adjacent sequences: A015450 A015451 A015452 * A015454 A015455 A015456`
	KEYWORD	`nonn,easy`
	AUTHOR	`Olivier Gerard (olivier.gerard(AT)gmail.com)`

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Last modified February 16 08:13 EST 2012. Contains 205893 sequences.