A152832 a(0) = -2; a(n) = n - a(n-1) for n > 0.

-2, 3, -1, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 9, 5, 10, 6, 11, 7, 12, 8, 13, 9, 14, 10, 15, 11, 16, 12, 17, 13, 18, 14, 19, 15, 20, 16, 21, 17, 22, 18, 23, 19, 24, 20, 25, 21, 26, 22, 27, 23, 28, 24, 29, 25, 30, 26, 31, 27, 32, 28, 33, 29, 34, 30, 35, 31, 36, 32, 37, 33, 38, 34, 39, 35

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A084964

Programs

Mathematica

lst={};a=2;Do[a=n-a;AppendTo[lst,a],{n,0,6!}];lst
RecurrenceTable[{a[0]==-2,a[n]==n-a[n-1]},a,{n,80}] (* or *) With[ {nn=40}, Riffle[ Range[-2,nn-2],Range[3,nn+3]]] (* Harvey P. Dale, Jun 02 2019 *)

Formula

From R. J. Mathar, Jan 03 2009, Aug 14 2009: (Start)

a(n) = (n+1)/2-(9*(-1)^n+1)/4.

G.f.: -(2*x-1)*(x-2)/((1+x)*(x-1)^2).

a(n) = a(n-1)+a(n-2)-a(n-3). (End)

Extensions

Definition corrected by N. J. A. Sloane, Jan 11 2009

Formula adapted to offset by R. J. Mathar, Aug 14 2009