The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A104544

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Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k HH's, where H=(1,0).
(history; published version)

#4 by Russ Cox at Fri Mar 30 17:36:01 EDT 2012

AUTHOR

_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Mar 14 2005

Discussion

Fri Mar 30

17:36

OEIS Server: https://oeis.org/edit/global/173

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

EXAMPLE

T(4,1)=3 because we have HHUD, UDHH, and UHHD, where U=(1,1), D=(1,-1) and H=(1,0).

KEYWORD

nonn,tabl,new

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

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

EXAMPLE

T(4,1)=3 because we have HHUD, UDHH, and UHHD, where U=(1,1), D=(1,-1), and H=(1,0).

KEYWORD

nonn,tabl,new

#1 by N. J. A. Sloane at Sat Apr 09 03:00:00 EDT 2005

NAME

Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k HH's, where H=(1,0).

DATA

1, 1, 1, 3, 0, 1, 5, 3, 0, 1, 11, 6, 3, 0, 1, 25, 13, 9, 3, 0, 1, 55, 40, 16, 12, 3, 0, 1, 129, 95, 60, 20, 15, 3, 0, 1, 303, 250, 155, 80, 25, 18, 3, 0, 1, 721, 661, 415, 235, 100, 31, 21, 3, 0, 1, 1743, 1708, 1206, 620, 335, 120, 38, 24, 3, 0, 1, 4241, 4515, 3262, 1946, 875, 455

OFFSET

1,4

FORMULA

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

EXAMPLE

Triangle starts:

1;

1,1;

3,0,1;

5,3,0,1;

11,6,3,0,1;

T(4,1)=3 because we have HHUD, UDHH, and UHHD, where U=(1,1), D=(1,-1), and H=(1,0).

CROSSREFS

Column 0 yields A104545. Row sums yield the Motzkin numbers (A001006).

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2005

STATUS

approved