login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339575 Triangle read by rows: T(n,k) is the number of cells in the k-th row of the diagram constructed in the fourth quadrant with the Dyck path described in the n-th row of A237593, 1 <= k <= n. 1
1, 2, 2, 3, 3, 2, 4, 4, 4, 3, 5, 5, 5, 3, 3, 6, 6, 6, 6, 5, 4, 7, 7, 7, 7, 5, 4, 4, 8, 8, 8, 8, 8, 6, 5, 5, 9, 9, 9, 9, 9, 7, 7, 5, 5, 10, 10, 10, 10, 10, 10, 8, 7, 6, 6, 11, 11, 11, 11, 11, 11, 8, 7, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 10, 10, 9, 7, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are the lengths of the rows if one regards the n-th region in the diagram as the Young diagram corresponding to a partition of A024916(n).

Column k gives the partial sums of the k-th column of triangle A240061. - Omar E. Pol, Dec 11 2020

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141, flattened)

Rémy Sigrist, PARI program for A339575

EXAMPLE

Triangle begins:

   1;

   2,  2;

   3,  3,  2;

   4,  4,  4,  3;

   5,  5,  5,  3,  3;

   6,  6,  6,  6,  5,  4;

   7,  7,  7,  7,  5,  4,  4;

   8,  8,  8,  8,  8,  6,  5,  5;

   9,  9,  9,  9,  9,  7,  7,  5,  5;

  10, 10, 10, 10, 10, 10,  8,  7,  6,  6;

  11, 11, 11, 11, 11, 11,  8,  7,  6,  6,  6;

  12, 12, 12, 12, 12, 12, 12, 10, 10,  9,  7,  7;

...

From Omar E. Pol, Jan 19 2022: (Start)

For n = 10 the Dyck path described in the 10th row of A237593 is as shown below in the fourth quadrant:

.

   k                                     10th row

      . . . . . . . . . . . . . X       of triangle

   1  .                    |                10

   2  .                    |                10

   3  .                    |                10

   4  .                    |                10

   5  .                    |                10

   6  .                 _ _|                10

   7  .               _|                     8

   8  .             _|                       7

   9  .            |                         6

  10  . _ _ _ _ _ _|                         6

      .

      .

     -y

.

T(10,k) is the number of cells in the k-th row of the diagram.

The total number of cells in all rows of the diagram is equal to A024916(10) = 87, the same as the sum of the 10th row of triangle. (End)

PROG

(PARI) See Links section.

CROSSREFS

Row sums are A024916.

Cf. A000203, A236104, A237270, A237591, A237593, A240061.

Sequence in context: A253900 A327487 A105496 * A167618 A211707 A303363

Adjacent sequences:  A339572 A339573 A339574 * A339576 A339577 A339578

KEYWORD

nonn,tabl,look

AUTHOR

N. J. A. Sloane, Dec 11 2020

EXTENSIONS

Name edited by Omar E. Pol, Jan 22 2022

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 15 02:07 EDT 2022. Contains 356122 sequences. (Running on oeis4.)