A117984 A modified Legendre-binomial transform of 4^n for p=3.

1, 3, 21, 63, 189, 1323, 4161, 12483, 87381, 262143, 786429, 5505003, 16515009, 49545027, 346815189, 1090777023, 3272331069, 22906317483, 68719738881, 206159216643, 1443114516501, 4329343549503, 12988030648509, 90916214539563

Offset

0,2

Comments

a(3n)=a(3n+1)/3=a(3n+2)/21; 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)=4^9-1 include a(0),a(1),a(2),a(3),a(4),a(6),a(7),a(8),a(9).

Links

Table of n, a(n) for n=0..23.

Formula

a(n)=sum{k=0..n, (-1)^(n-k)*L(C(n,k)/3)*4^k} where L(j/p) is the Legendre symbol of j and p.

Crossrefs

Sequence in context: A354850 A328042 A331082 * A050615 A145658 A342548

Adjacent sequences: A117981 A117982 A117983 * A117985 A117986 A117987

Keyword

easy,nonn

Author

Paul Barry, Apr 06 2006

Status

approved