A048575 - OEIS

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A048575

Pisot sequences L(2,5), E(2,5).

2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437, 1134903170, 2971215073, 7778742049, 20365011074, 53316291173, 139583862445, 365435296162, 956722026041 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,1`
	LINKS	`Index entries for sequences related to linear recurrences with constant coefficients` `Tanya Khovanova, Recursive Sequences`
	FORMULA	`a(n) = Fib(2n+3). a(n) = 3a(n-1) - a(n-2).` `G.f.: (2-x)/(1-3x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]` `a(n)=[(3/2)+(1/2)sqrt(5)]^n+(2/5)[(3/2)+(1/2)sqrt(5)]^nsqrt(5)-(2/5)[(3/2)-(1/2)sqrt(5)]^n sqrt(5)+[(3/2)-(1/2)sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 20 2008]`
	CROSSREFS	`Subsequence of A001519. See A008776 for definitions of Pisot sequences.` `Sequence in context: A001519 A122367 * A099496 A114299 A112842 A097417` `Adjacent sequences: A048572 A048573 A048574 * A048576 A048577 A048578`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson (davidwwilson(AT)comcast.net)`

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Last modified February 13 06:15 EST 2012. Contains 205438 sequences.