A100736 Inverse modulo 2 binomial transform of 3^n.

1, 2, 8, 16, 80, 160, 640, 1280, 6560, 13120, 52480, 104960, 524800, 1049600, 4198400, 8396800, 43046720, 86093440, 344373760, 688747520, 3443737600, 6887475200, 27549900800, 55099801600, 282386483200, 564772966400

Offset: 0

Author

Paul Barry, Dec 06 2004

Keywords

• easy
• nonn

Comments

3^n may be retrieved as Sum_{k=0..n} (binomial(n,k) mod 2)*A100736(k).

Crossrefs

Cf. A010060, A100735.

Programs

PARI

a(n)=abs(sum(k=0, n, (-1)^(hammingweight(k)%2)* lift(Mod(binomial(n, k), 2))*3^k)) \\ Jianing Song, Jan 27 2019

Formula

a(n) = Sum_{k=0..n} (-1)^A010060(n-k)*(binomial(n, k) mod 2)*3^k.