A117980 Legendre-binomial transform of (-1)^n for p=3.

1, 0, 3, 0, 0, 0, 3, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 9, 0, 0, 0, 9, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 9, 0, 0, 0, 9, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 27, 0, 0, 0, 27, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,3

Comments

a(n)=a(3n)=a(3n+2)/3; a(3n+2)=0.

Links

Antti Karttunen, Table of n, a(n) for n = 0..19683

Formula

a(n)=sum{k=0..n, L(C(n,k)/3)*(-1)^k} where L(j/p) is the Legendre symbol of j and p.

Prog

(PARI) A117980(n) = sum(k=0, n, kronecker(binomial(n, k), 3)*((-1)^k)); \\ Antti Karttunen, Sep 20 2019

Crossrefs

Sequence in context: A219551 A200221 A158678 * A065032 A007514 A336642

Adjacent sequences: A117977 A117978 A117979 * A117981 A117982 A117983

Keyword

easy,nonn

Author

Paul Barry, Apr 06 2006

Status

approved