The On-Line Encyclopedia of Integer Sequences (OEIS)

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A127832

Array T by antidiagonals: for h>=0 and k>=0, T(h,k)=number of UR paths from (0,0) to (h,k) that touch the line y=2x/3 only at lattice points. A UR path is a path of steps of length 1 each directed up or right.
(history; published version)

#2 by Russ Cox at Fri Mar 30 18:57:10 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Feb 01 2007

Discussion

Fri Mar 30

18:57

OEIS Server: https://oeis.org/edit/global/285

#1 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

NAME

Array T by antidiagonals: for h>=0 and k>=0, T(h,k)=number of UR paths from (0,0) to (h,k) that touch the line y=2x/3 only at lattice points. A UR path is a path of steps of length 1 each directed up or right.

DATA

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 4, 5, 4, 3, 1, 1, 5, 9, 9, 7, 4, 1, 1, 6, 14, 18, 9, 11, 5, 1, 1, 7, 20, 32, 27, 11, 16, 6, 1, 1, 8, 27, 52, 59, 27, 27, 22, 7, 1, 1, 9, 35, 79, 111, 86, 54, 49, 29, 8, 1, 1, 10, 44, 114, 190, 197, 140, 103, 78, 37, 9, 1, 1, 11, 54, 158, 304, 387

OFFSET

1,8

EXAMPLE

Northwest corner:

0 1 1 1 1 1

1 1 2 3 4 5

1 1 2 5 9 14

1 2 4 9 18 32

1 3 7 9 27 59

The 4 UR paths for T(3,2) are RRRUU, RRURU, UURRR, URURR. These

paths touch the line y=2x/3 only at the lattice points (0,0) and (3,2).

CROSSREFS

Cf. A047110, A127833.

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Feb 01 2007

STATUS

approved