The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,1 LINKS 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) 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_] := 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}] 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 21:57 EST 2022. Contains 358453 sequences. (Running on oeis4.)