A082507 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.

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, 13, 11, 11, 11, 14, 12, 12, 12, 15, 13, 13, 13, 16, 14, 14, 14, 17, 15, 15, 15, 18, 16, 16, 16, 19, 17, 17, 17, 20, 18, 18

Offset

-1,1

Links

Amiram Eldar, Table of n, a(n) for n = -1..10000

Formula

From R. J. Mathar, Aug 22 2008: (Start)

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. (End)

Example

The 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.
The value of a(-1) = 2 is arbitrary but provides a suitable extension.

Mathematica

f[x_] := f[x] = x-f[x-1]-f[x-2]-f[x-3]; {f[-1]=2, f[0]=0, f[1]=0, f[2]=0}; Table[f[w], {w, -1, 25}]

Crossrefs

Cf. A063942, A028242, A001057.

Sequence in context: A386791 A392491 A113503 * A132349 A216226 A123391

Adjacent sequences: A082504 A082505 A082506 * A082508 A082509 A082510

Keyword

nonn

Author

Labos Elemer, Apr 28 2003

Extensions

More terms from Amiram Eldar, Mar 16 2025

Status

approved