A309215 a(0)=0; thereafter a(n) = a(n-1)+n if a(n-1) odd, otherwise a(n) = a(n-1)-n.

0, -1, 1, 4, 0, -5, 1, 8, 0, -9, 1, 12, 0, -13, 1, 16, 0, -17, 1, 20, 0, -21, 1, 24, 0, -25, 1, 28, 0, -29, 1, 32, 0, -33, 1, 36, 0, -37, 1, 40, 0, -41, 1, 44, 0, -45, 1, 48, 0, -49, 1, 52, 0, -53, 1, 56, 0, -57, 1, 60, 0, -61, 1, 64, 0, -65, 1, 68, 0, -69, 1, 72, 0, -73, 1, 76, 0, -77

Offset: 0

Author

N. J. A. Sloane, Aug 10 2019

Keywords

• sign
• easy

Comments

A003816 and A309214 have the same terms except for signs.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-2,2,-1,1).

Crossrefs

Cf. A003816, A309529, A309214, A309216, A309217.

Programs

Maple

t:=0;
a:=[t]; M:=100;
for i from 1 to M do
if (t mod 2) = 1 then t:=t+i else t:=t-i; fi;
a:=[op(a),t]; od:
a;

Mathematica

nxt[{n_,a_}]:={n+1,If[OddQ[a],a+n+1,a-n-1]}; NestList[nxt,{0,0},80][[All,2]] (* Harvey P. Dale, Sep 26 2021 *)

PARI

concat(0, Vec(-x*(1 - 2*x - x^2) / ((1 - x)*(1 + x^2)^2) + O(x^40))) \\ Colin Barker, Aug 13 2019

Formula

a(4t)=0, a(4t+1)=-(4t+1), a(4t+2)=1, a(4t+3)=4t+4.

From Colin Barker, Aug 13 2019: (Start)

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

a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) + a(n-5) for n>4.

a(n) = 1/2 - (1/4 - i/4)*((-i)^n+i^(1+n)) - (1/2)*i*((-i)^n-i^n)*(1+n) where i=sqrt(-1).

(End)