A164303 - OEIS

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A164303

a(n) = 2*a(n-1)+a(n-2) for n > 1; a(0) = 3, a(1) = 11.

3, 11, 25, 61, 147, 355, 857, 2069, 4995, 12059, 29113, 70285, 169683, 409651, 988985, 2387621, 5764227, 13916075, 33596377, 81108829, 195814035, 472736899, 1141287833, 2755312565, 6651912963, 16059138491, 38770189945, 93599518381 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,1`
	COMMENTS	`Binomial transform of A164654. Inverse binomial transform of A164304.`
	LINKS	`Vincenzo Librandi, Table of n, a(n) for n = 0..218`
	FORMULA	`a(n) = 2a(n-1)+a(n-2) for n > 1; a(0) = 3, a(1) = 11.` `a(n) = ((3+4sqrt(2))(1+sqrt(2))^n+(3-4sqrt(2))(1-sqrt(2))^n)/2.` `G.f.: (3+5x)/(1-2*x-x^2).`
	PROG	`(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4r)(1+r)^n+(3-4r)(1-r)^n)/2: n in [0..28] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Aug 20 2009]`
	CROSSREFS	`Cf. A164654, A164304.` `Sequence in context: A147382 A212971 A184634 * A129082 A190476 A060746` `Adjacent sequences: A164300 A164301 A164302 * A164304 A164305 A164306`
	KEYWORD	`nonn,easy`
	AUTHOR	`Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009`
	EXTENSIONS	`Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009`
	STATUS	`approved`

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Last modified May 19 19:08 EDT 2013. Contains 225436 sequences.