A117976 Legendre-binomial transform of 2^n for p=3.

1, 3, 3, 9, 27, 27, 57, 171, 171, 513, 1539, 1539, 4617, 13851, 13851, 29241, 87723, 87723, 261633, 784899, 784899, 2354697, 7064091, 7064091, 14913081, 44739243, 44739243, 134217729, 402653187, 402653187, 1207959561

Offset

0,2

Comments

a(3n)=a(3n+1)/a(1)=a(3n+2)/a(2); a(9n)=a(9n+3)/a(3)=a(9n+6)/a(6); a(27n)=a(27n+9)/a(9)=a(27n+18)/a(18); a(3^k*n)=a(3^k*n+3^(k-1))/a(3^(k-1))=a(3^k*n+2*3^(k-1))/a(2*3^(k-1)), k>0.

Links

Table of n, a(n) for n=0..30.

Formula

a(n)=sum{k=0..n, L(C(n,k)/3)*2^k} where L(j/p) is the Legendre symbol of j and p.

Crossrefs

Sequence in context: A083008 A268092 A229024 * A010098 A029857 A327712

Adjacent sequences: A117973 A117974 A117975 * A117977 A117978 A117979

Keyword

easy,nonn

Author

Paul Barry, Apr 06 2006

Status

approved