A097888 - OEIS

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A097888

Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k high humps. (A hump is an upstep followed by 0 or more flatsteps followed by a downstep. A high hump is a hump that starts at a level higher than zero.).

1, 1, 2, 4, 8, 1, 16, 5, 32, 18, 1, 64, 56, 7, 128, 160, 34, 1, 256, 432, 138, 9, 512, 1120, 500, 55, 1, 1024, 2816, 1672, 275, 11, 2048, 6912, 5264, 1205, 81, 1, 4096, 16640, 15808, 4797, 481, 13, 8192, 39424, 45696, 17738, 2471, 112, 1, 16384, 92160, 128000

(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..53.

FORMULA

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

EXAMPLE

Triangle begins:

8,1;