

A082507


Generated by a 3rdorder formal recursion with suitable initial values as follows: a(n) = n  a(n1)  a(n2)  a(n3); a(0)=a(1)=a(2)=0.


0



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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..42.


FORMULA

From R. J. Mathar, Aug 22 2008: (Start)
O.g.f.: 2/x+x^3(32x)/((1x)^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. (End)
a(n) = 3/8 + (1/8)*(1 + 5*i)*i^n  (5/8)*(1)^n + (1/4)*n + (1/8)*(1  5*i)*(i)^n, with n >= 1, where i=sqrt(1).  Paolo P. Lava, Jul 09 2010


EXAMPLE

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 provides a suitable extension.


MATHEMATICA

f[x_] := xf[x1]f[x2]f[x3]; {f[0]=0, f[1]=0, f[2]=0}; Table[f[w], {w, 1, 25}]


CROSSREFS

Cf. A063942, A028242, A001057.
Sequence in context: A327172 A355524 A113503 * A132349 A216226 A123391
Adjacent sequences: A082504 A082505 A082506 * A082508 A082509 A082510


KEYWORD

nonn


AUTHOR

Labos Elemer, Apr 28 2003


STATUS

approved



