A138016 Row sums of triangle A138015.

1, 2, 4, 6, 10, 14, 24, 34, 68, 102, 256, 410, 1284, 2158, 8072, 13986, 60220, 106454, 515568, 924682, 4962596, 9000510, 52955224, 96909938, 619866252, 1142822566, 7892799680, 14642776794, 108571045108, 202499313422, 1604101949736, 3005704586050, 25330097110364, 47654489634678

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Formula

a(n) = Sum_{k=1..n} A003422(ceiling(k/2)).

a(2*n) = 2*A014144(n); a(2*n+1) = 2*A014144(n) + A003422(n+1). - Andrew Howroyd, Sep 21 2025

Example

a(5) = 10 = sum of row 5 terms of triangle A138015: (1 + 2 + 4 + 2 + 1).
a(5) = 10 = (1 + 1 + 2 + 2 + 4) since A003422 starting (1, 2, 4, 10, 34, 154, ...) then repeating each term = (1, 1, 2, 2, 4, 4, 10, 10, ...). Take partial sums of the first 5 terms.

Prog

(PARI) a(n) = sum(k=0, n\2-1, (n-2*k)*k!) + if(n%2, (n\2)!) \\ Andrew Howroyd, Sep 21 2025

Crossrefs

Cf. A003422, A014144, A138015.

Sequence in context: A395588 A364671 A280611 * A239787 A113118 A287636

Adjacent sequences: A138013 A138014 A138015 * A138017 A138018 A138019

Keyword

nonn

Author

Gary W. Adamson, Feb 28 2008

Extensions

a(17) onwards from Andrew Howroyd, Sep 21 2025

Status

approved