A097892 - OEIS

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A097892

Triangle read by rows: T(n,k) is the number of Motzkin paths of length n and having k peaks at even height.

1, 1, 2, 4, 8, 1, 17, 4, 38, 12, 1, 88, 34, 5, 209, 95, 18, 1, 506, 264, 59, 6, 1244, 731, 187, 25, 1, 3097, 2020, 582, 92, 7, 7791, 5578, 1786, 322, 33, 1, 19773, 15404, 5420, 1096, 134, 8, 50563, 42558, 16308, 3652, 510, 42, 1, 130149, 117652, 48744, 11960, 1872

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Row sums are the Motzkin numbers (A001006).

LINKS

Table of n, a(n) for n=0..55.

FORMULA

G.f.=G=G(t, z) satisfies z^2*(1-z)G^2-(1-z)(1-z+z^2-tz^2)G+1-z+z^2-tz^2=0.

EXAMPLE

Triangle begins:

8,1;