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A112657 A Motzkin transform of Jacobsthal numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 10:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)