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A133405 a(n) = 3*a(n-1) - a(n-3) + 3*a(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

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 May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)