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A127742 Triangle read by rows with shape A000041 which refines the Catalan triangle A033184 using sequence A048996. 2
1, 1, 1, 2, 2, 1, 5, 4, 1, 3, 1, 14, 10, 4, 6, 3, 4, 1, 42, 28, 10, 4, 15, 12, 1, 8, 6, 5, 1, 132, 84, 28, 20, 42, 30, 12, 6, 20, 24, 4, 10, 10, 6, 1, 429, 264, 84, 56, 25, 126, 84, 60, 15, 12, 56, 60, 24, 24, 1, 25, 40, 10, 12, 15, 7, 1, 1430, 858, 264, 168, 140, 396, 252, 168, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Contribution from R. J. Mathar, Jul 16 2010: (Start)

The entries count Dyck paths of length 2n which have a step/stride pattern between consecutive returns to the horizontal axes (after sorting) equivalent to the k-th partition of n.

Equivalent means that each distance between two x (where y=0) is divided by 2 prior to comparison.

Example: if the x-values are (0,4,8,10,16) with 2n=16, the strides are 4,4,2,6, equal to 2,2,1,3 after division by 2, and contribute to the 1^1,2^2,3^1 partition T(8,14). (End)

LINKS

Table of n, a(n) for n=1..75.

EXAMPLE

The triangle begins

1

1 1

2 2 1

5 4 1 3 1

14 10 4 6 3 4 1

etc

CROSSREFS

Sequence in context: A134226 A184050 A226059 * A110438 A184051 A121460

Adjacent sequences:  A127739 A127740 A127741 * A127743 A127744 A127745

KEYWORD

nonn,tabf

AUTHOR

Alford Arnold, Feb 23 2007

EXTENSIONS

More terms from R. J. Mathar, Jul 16 2010

STATUS

approved

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)