A305029 Period 10 sequence [ 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, ...] except a(0) = 1.

1, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, 0, 2, 2, 2, 2, 0, -2, -2, -2, -2

Offset: 0

Author

Seiichi Manyama, May 24 2018

Keywords

• easy
• sign

Comments

If m is odd, (Sum_{k=0..m} x^k)/(Sum_{k=0..m} (-x)^k) = (1+x)/(1-x).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A040000 (m is odd), A000007 (m=0), A184334 (m=2), this sequence (m=4).

Programs

PARI

N=66; x='x+O('x^N); Vec(((sum(k=0, 4, x^k))/(sum(k=0, 4, (-x)^k))))

Formula

G.f.: (1 + x + x^2 + x^3 + x^4)/(1 - x + x^2 - x^3 + x^4).