A112657 A Motzkin transform of Jacobsthal numbers.

1, 2, 7, 23, 79, 272, 943, 3278, 11419, 39830, 139057, 485795, 1697905, 5936348, 20760271, 72615143, 254028355, 888758030, 3109714117, 10881403229, 38077702909, 133251869648, 466325356273, 1631981113112, 5711490384901

Offset

0,2

Comments

Binomial transform of A100098.

Inverse binomial transform of A007854. The Hankel transform of this sequence is 3^n (see A000244). - Philippe Deléham, Nov 25 2007

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..n} A026300(n, k)*(2^(k+1) + (-1)^k)/3, where A026300 is the Motzkin triangle; a(n) = Sum_{k=0..n} ((k+1)/(n+1))*Sum_{j=0..n+1} C(n+1, j)*C(j, 2j-n+k)*(2^(k+1) + (-1)^k)/3.

a(n) = Sum_{k=0..n} A089942(n,k)*2^k = Sum_{k=0..n} A071947(n,k)*2^(n-k). - Philippe Deléham, Mar 31 2007

Crossrefs

Cf. A000244, A007854, A026300, A089942, A100098.

Sequence in context: A068593 A198944 A328035 * A007717 A130567 A091514

Adjacent sequences: A112654 A112655 A112656 * A112658 A112659 A112660

Keyword

easy,nonn

Author

Paul Barry, Jan 11 2006

Status

approved