A358492 - OEIS

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A358492

Irregular triangle read by rows: T(n,k) is one half of the number of line segments of length 1 in the k-th antidiagonal of the Dyck path described in the n-th row of A237593.

1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 1, 3, 2, 1, 1, 1, 3, 3, 1, 1, 1, 1, 4, 2, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 1, 3, 4, 1, 1, 1, 1, 3, 4, 2, 1, 1, 1, 1, 2, 4, 2, 2, 1, 1, 1, 1, 1, 3, 5, 2, 1, 1, 1, 1, 1, 1, 3, 5, 2, 1, 1, 1, 1, 1, 3, 5, 2, 2, 1, 1, 1, 1, 1, 1, 1, 5, 4, 2, 1, 1, 1, 1, 1, 1, 5, 4, 2, 2

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..109.

EXAMPLE

Triangle begins (first 19 rows):

1, 1;

1, 2;

1, 1, 2;

1, 2, 2;

1, 1, 1, 3;

1, 1, 3, 2;

1, 1, 1, 3, 2;

1, 1, 1, 3, 3;

1, 1, 1, 1, 4, 2;

1, 1, 1, 4, 2, 2;

1, 1, 1, 1, 1, 3, 4;

1, 1, 1, 1, 3, 4, 2;

1, 1, 1, 1, 2, 4, 2, 2;

1, 1, 1, 1, 1, 3, 5, 2;

1, 1, 1, 1, 1, 1, 3, 5, 2;

1, 1, 1, 1, 1, 3, 5, 2, 2;

1, 1, 1, 1, 1, 1, 1, 5, 4, 2;

1, 1, 1, 1, 1, 1, 5, 4, 2, 2;

...

For n = 10 the 10th row of A237593 is [6, 2, 1, 1, 1, 1, 2, 6]. When that row is interpreted as a symmetric Dyck path in the fourth quadrant using 20 line segments of length 1 the Dyck path looks like this:

_ _|

_ _ _ _ _ _|

The numbers of line segments of length 1 in the successive antidiagonals are respectively [2, 2, 2, 2, 8, 4] so the 10th row of triangle is [1, 1, 1, 1, 4, 2].

CROSSREFS

Row sums give A000027.

Row n has length A008619(n).

Column 1 gives A000012.

Cf. A196020, A235791, A236104, A237270, A237271, A237591, A237593, A245092, A262626, A339575.

Sequence in context: A091591 A376361 A337633 * A227796 A109374 A079706

Adjacent sequences: A358489 A358490 A358491 * A358493 A358494 A358495

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Nov 19 2022

STATUS

approved