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A071408
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a(n+1) - 2*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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1
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0, 1, 4, 7, 10, 15, 20, 25, 32, 39, 46, 55, 64, 73, 84, 95, 106, 119, 132, 145, 160, 175, 190, 207, 224, 241, 260, 279, 298, 319, 340, 361, 384, 407, 430, 455, 480, 505, 532, 559, 586, 615, 644, 673, 704, 735, 766, 799, 832, 865, 900, 935, 970, 1007, 1044
(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. Beginning with a(2) the first differences are 3,3,3,5,5,5,7,7,7,9,9,9,11, etc.
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FORMULA
| a(n) = floor(n*(n+2)*(n+4)/(3n+6)), with offset 0 [From Gary Detlefs (gdetlefs(AT)aol.com), Jul 13 2010]
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MATHEMATICA
| a[1] = 0; a[2] = 1; w = Exp[2Pi*I/3]; a[n_] := a[n] = Simplify[(2/3)(1 + w^n + w^(2n)) + 2a[n - 1] - a[n - 2]]; Table[ a[n], {n, 1, 60}]
Table[If[n<3, n-1, Floor[((n+1)^2-4)/3]], {n, 1, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)
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CROSSREFS
| Cf. A071618, A032765(n)-1.
Sequence in context: A014690 A126891 A095875 * A137461 A137379 A096676
Adjacent sequences: A071405 A071406 A071407 * A071409 A071410 A071411
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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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