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A072130 a(n+1) -3*a(n) + a(n-1) = (2/3)*(1+w^(n+1)+w^(2*n+2)); a(1) = 0, a(2) = 1; where w is the cubic root of unity. 0
0, 1, 5, 14, 37, 99, 260, 681, 1785, 4674, 12237, 32039, 83880, 219601, 574925, 1505174, 3940597, 10316619, 27009260, 70711161, 185124225, 484661514, 1268860317, 3321919439, 8696898000, 22768774561, 59609425685, 156059502494 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

w = exp(2Pi*I/3) = (-1-Sqrt(-3))/2.

The sequence (2/3)*(1+w^(n+1)+w^(2*n+2)) is "Period 3: repeat [0,2,0]."

LINKS

Table of n, a(n) for n=1..28.

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

FORMULA

G.f.: x^2*(1+x)*(1+x-x^2)/((1-x)*(1-3*x+x^2)*(1+x+x^2)). [Colin Barker, Jan 14 2012]

a(1)=0, a(2)=1, a(3)=5, a(4)=14, a(5)=37, a(n)=3*a(n-1)- a(n-2)+ a(n-3)-3*a(n-4)+a(n-5). - Harvey P. Dale, Aug 19 2012

MATHEMATICA

a[1] = 0; a[2] = 1; w = Exp[2Pi*I/3]; a[n_] := (2/3)(1 + w^n + w^(2n)) + 3a[n - 1] - a[n - 2]; Table[ Simplify[ a[n]], {n, 1, 28}]

LinearRecurrence[{3, -1, 1, -3, 1}, {0, 1, 5, 14, 37}, 30] (* Harvey P. Dale, Aug 19 2012 *)

CROSSREFS

Cf. A071618.

Sequence in context: A224716 A127980 A054486 * A196976 A045553 A270687

Adjacent sequences:  A072127 A072128 A072129 * A072131 A072132 A072133

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 24 2002

STATUS

approved

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Last modified June 16 05:18 EDT 2019. Contains 324145 sequences. (Running on oeis4.)