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Search: id:A072130
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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
1
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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
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OFFSET
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1,3
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COMMENT
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w = exp(2Pi*I/3) = (-1-Sqrt(-3))/2.
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MATHEMATICA
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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
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Cf. A071618.
Sequence in context: A048745 A127980 A054486 this_sequence A045553 A111715 A024525
Adjacent sequences: A072127 A072128 A072129 this_sequence A072131 A072132 A072133
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 24 2002
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