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A133405 a(n)=3a(n-1)-a(n-3)+3a(n-4). 2
0, 0, 0, 1, 3, 9, 26, 78, 234, 703, 2109, 6327, 18980, 56940, 170820, 512461, 1537383, 4612149, 13836446, 41509338, 124528014, 373584043, 1120752129, 3362256387, 10086769160, 30260307480, 90780922440, 272342767321, 817028301963, 2451084905889, 7353254717666 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (3, 0, -1, 3).

FORMULA

a(n+1)-3a(n)=hexaperiodic 0, 0, 1, 0, 0, -1, A131531.

O.g.f.: -x^3/((3*x-1)*(x+1)*(x^2-x+1)) = -(1/28)/(3*x-1)-(1/12)/(x+1)+(1/21)*(-5*x+1)/(x^2-x+1) . - R. J. Mathar, Nov 28 2007

a(n)=(1/42)*{1/2-(1/2)*I*sqrt(3)}^n+(1/28)*3^n-(1/12)*(-1)^n+(1/42)*{1/2+(1/2)*I*sqrt(3)}^n -(1/14)*I*{1/2-(1/2)*I*sqrt(3)}^n*sqrt(3)+(1/14)*I*{1/2+(1/2)*I*sqrt(3)}^n *sqrt(3), with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 09 2008

MATHEMATICA

LinearRecurrence[{3, 0, -1, 3}, {0, 0, 0, 1}, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)

CROSSREFS

Sequence in context: A027915 A295115 A114982 * A196952 A148921 A148922

Adjacent sequences:  A133402 A133403 A133404 * A133406 A133407 A133408

KEYWORD

nonn

AUTHOR

Paul Curtz, Nov 24 2007

STATUS

approved

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Last modified July 11 15:58 EDT 2020. Contains 335626 sequences. (Running on oeis4.)