id:A082841 - OEIS Search Results

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a(n)=4a(n-1)-a(n-2).

+0
6

3, 9, 33, 123, 459, 1713, 6393, 23859, 89043, 332313, 1240209, 4628523, 17273883, 64467009, 240594153, 897909603, 3351044259, 12506267433, 46674025473, 174189834459, 650085312363, 2426151414993, 9054520347609, 33791929975443 (list; graph; listen)

	OFFSET	`0,1`
	LINKS	`Index entries for sequences related to linear recurrences with constant coefficients` `Tanya Khovanova, Recursive Sequences`
	FORMULA	`G.f.: (3-6x+3x^2)/((1-x)(1-4x+x^2)). With a=2+sqrt(3), b=2-sqrt(3): a(n)=sqrt(3/2)(a^(n+1/2)+b^(n+1/2)). a(n)=sqrt(3(11+12A082840(n)+4A082840(n)^2)). a(n)=sqrt((3/2)(A003500(2n+1)+2)). a(n)-a(n-1)=6*A001353(n). a(n)=3 (mod 6)`
	MATHEMATICA	`CoefficientList[Series[(3-6 x+3 x^2)/((1-x)(1-4 x+x^2)), {x, 0, 25}], x]`
	CROSSREFS	`First differences of A005320.` `Equals 3 * A001835(n+1).` `Sequence in context: A148995 A148996 A148997 this_sequence A151038 A039648 A049182` `Adjacent sequences: A082838 A082839 A082840 this_sequence A082842 A082843 A082844`
	KEYWORD	`easy,nonn`
	AUTHOR	`Mario Catalani (mario.catalani(AT)unito.it), Apr 14 2003`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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