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A305029 Period 10 sequence [ 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, ...] except a(0) = 1. 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 (list; graph; refs; listen; history; text; internal format)
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).

a(n) = C(2*n,n) mod 2 + 1/5*(-(n mod 10)+((n+4) mod 10)+((n+5) mod 10)-((n+9) mod 10)). - Paolo P. Lava, Jun 08 2018

MAPLE

1, seq(1/5*(-(n mod 10)+((n+4) mod 10)+((n+5) mod 10)-((n+9) mod 10)), n=1..80); # Paolo P. Lava, Jun 08 2018

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

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Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)