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

0,2

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

Formula

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

Prog

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

Crossrefs

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

Sequence in context: A065833 A245476 A215884 * A097033 A268686 A113306

Adjacent sequences: A305026 A305027 A305028 * A305030 A305031 A305032

Keyword

easy,sign

Author

Seiichi Manyama, May 24 2018

Status

approved