A034929 A triangle of Motzkin ballot numbers, read by rows.

1, 1, 1, 1, 2, 1, 1, 3, 3, 2, 1, 4, 6, 6, 4, 1, 5, 10, 13, 13, 9, 1, 6, 15, 24, 30, 30, 21, 1, 7, 21, 40, 59, 72, 72, 51, 1, 8, 28, 62, 105, 148, 178, 178, 127, 1, 9, 36, 91, 174, 276, 378, 450, 450, 323, 1, 10, 45, 128, 273, 480, 730, 980, 1158, 1158, 835, 1, 11, 55, 174, 410, 791

Offset

1,5

Comments

Mirror image of A091836. Row sums are the Motzkin numbers (A001006). T(n,n-1)=A001006(n-2) (the Motzkin numbers). T(n,n-2)=A005554(n-1).

References

M. Aigner, Motzkin numbers, Europ. J. Comb. 19 (1998), 663-675.

Links

Table of n, a(n) for n=1..72.

Formula

G.f.= 2(1+tz)/[1-2z+tz-2tz^2+sqrt(1-2tz-3t^2*z^2)].

Example

Triangle begins:
[1],
[1, 1],
[1, 2, 1],
[1, 3, 3, 2],
[1, 4, 6, 6, 4],
[1, 5, 10, 13, 13, 9],
[1, 6, 15, 24, 30, 30, 21],
[1, 7, 21, 40, 59, 72, 72, 51]

Crossrefs

Cf. A001006, A091836, A005554.

Sequence in context: A215065 A175424 A144401 * A099509 A153859 A363394

Adjacent sequences: A034926 A034927 A034928 * A034930 A034931 A034932

Keyword

nonn,tabl

Author

N. J. A. Sloane.

Extensions

Edited by Emeric Deutsch, Mar 11 2004

Status

approved