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A072130
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a(n+1) -3*a(n) + a(n-1) = (2/3)(1+w^(n+1)+w^(2n+2)); a(1) = 0, a(2) = 1; where w is the imaginary cubic root of unity.
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0
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| w = exp(2Pi*I/3) = (-1-Sqrt(-3))/2.
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FORMULA
| Empirical 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]
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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}]
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CROSSREFS
| Cf. A071618.
Sequence in context: A048745 A127980 A054486 * A196976 A045553 A183898
Adjacent sequences: A072127 A072128 A072129 * A072131 A072132 A072133
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 24 2002
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