A117983 A modified Legendre-binomial transform of 2^n for p=3.

1, 2, 13, 26, 52, 338, 757, 1514, 9841, 19682, 39364, 255866, 511732, 1023464, 6652516, 14899274, 29798548, 193690562, 387440173, 774880346, 5036722249, 10073444498, 20146888996, 130954778474, 293292210961, 586584421922

Offset

0,2

Comments

a(3n)=a(3n+1)/2=a(3n+2)/13; 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. Divisors of a(9)=3^9-1 are a(0),a(1),a(2),a(3),a(6),a(7),a(8),a(9).

Links

Table of n, a(n) for n=0..25.

Formula

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

Crossrefs

Sequence in context: A018657 A161711 A018745 * A367265 A274869 A018400

Adjacent sequences: A117980 A117981 A117982 * A117984 A117985 A117986

Keyword

easy,nonn

Author

Paul Barry, Apr 06 2006

Status

approved