A201823 Terms of A001764 not divisible by 3, where A001764 enumerates ternary trees.

1, 1, 55, 300830572, 1414282077098335379544565517191

Offset

0,3

Comments

The number of digits for the terms begin:

[1, 1, 2, 9, 31, 97, 298, 902, 2715, 8155, 24478, 73446, 220354, ...].

Links

Table of n, a(n) for n=0..4.

Formula

a(n) = A001764( (3^n-1)/2 ) = binomial( 3*(3^n-1)/2, (3^n-1)/2 ) / 3^n.

a(n) == 1 (mod 3).

Example

Sequence A001764 begins: [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675, ...],
where A001764(n) == 1 (mod 3) at positions: [0, 1, 4, 13, 40, 121, 364, 1093, ...].

Prog

(PARI) a(n)=binomial(3*(3^n-1)/2, (3^n-1)/2)/3^n

Crossrefs

Cf. A038003, A001764.

Sequence in context: A172856 A093255 A172896 * A115410 A250489 A308097

Adjacent sequences: A201820 A201821 A201822 * A201824 A201825 A201826

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2011

Status

approved