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Search: id:A082507
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| A082507 |
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Generated by a 3rd-order formal recursion with suitable initial values as follows: a[n]=n-a[n-1]-a[n-2]-a[n-3]; a[0]=a[1]=a[2]=0. |
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+0
1
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| 2, 0, 0, 0, 3, 1, 1, 1, 4, 2, 2, 2, 5, 3, 3, 3, 6, 4, 4, 4, 7, 5, 5, 5, 8, 6, 6, 6, 9, 7, 7, 7, 10, 8, 8, 8, 11, 9, 9, 9, 12, 10, 10, 10
(list; graph; listen)
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OFFSET
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-1,1
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FORMULA
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O.g.f.: 2/x+x^3(3-2x)/((1-x)^2*(1+x)(1+x^2)). a(n) = 3/8 -5*(-1)^n/8 +n/4 +(1/4)*cos(Pi*n/2) -(5/4)*sin(Pi*n/2), n>-1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2008]
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EXAMPLE
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Sum of 4 successive terms gives n for n>2:
n=2=a(-1)+a(0)+a(1)+a(2)=2+0+0+0;
n=3=a(3)=a(0)+a(1)+a(2)+a(3)=0+0+0+3;
n=4=a(1)+a(2)+a(3)+a(4)=0+0+3+1;
Value of a(-1)=2 is arbitrary but provide suitable extension.
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MATHEMATICA
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f[x_] := x-f[x-1]-f[x-2]-f[x-3]; {f[0]=0, f[1]=0, f[2]=0}; Table[f[w], {w, 1, 25}]
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CROSSREFS
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Cf. A063942, A028242, A001057.
Sequence in context: A083059 A046268 A113503 this_sequence A132349 A123391 A076260
Adjacent sequences: A082504 A082505 A082506 this_sequence A082508 A082509 A082510
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 28 2003
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