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A182285 Triangle read by rows: T(n,k) = sum of all parts in the k-th zone of the last section of the set of partitions of n. 1
1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row n lists A000041(n-1) 1's together with A002865(n) n's.

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

Illustration of three arrangements of the last section of the set of partitions of 7 and the zone numbers:

--------------------------------------------------------

Zone \   a)                    b)                    c)

--------------------------------------------------------

15      (7)                   (7)       (. . . . . . 7)

14      (4+3)               (4+3)       (. . . 4 . . 3)

13      (5+2)               (5+2)       (. . . . 5 . 2)

12      (3+2+2)           (3+2+2)       (. . 3 . 2 . 2)

11        (1)                 (1)                   (1)

10          (1)               (1)                   (1)

9           (1)               (1)                   (1)

8             (1)             (1)                   (1)

7           (1)               (1)                   (1)

6             (1)             (1)                   (1)

5             (1)             (1)                   (1)

4               (1)           (1)                   (1)

3               (1)           (1)                   (1)

2                 (1)         (1)                   (1)

1                   (1)       (1)                   (1)

.

For n = 7 and k = 12 we can see that in the 12th zone of the last section of 7 the parts are 3, 2, 2, therefore T(7,12) = 3+2+2 = 7.

Written as a triangle begins:

1;

1,2;

1,1,3;

1,1,1,4,4;

1,1,1,1,1,5,5;

1,1,1,1,1,1,1,6,6,6,6;

1,1,1,1,1,1,1,1,1,1,1,7,7,7,7;

1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,8,8,8,8;

CROSSREFS

Row n has length A000041(n). Row sums give A138879.

Cf. A000041, A002865, A135010, A138121, A182284, A193173.

Sequence in context: A108888 A124021 A109626 * A160182 A195825 A098824

Adjacent sequences:  A182282 A182283 A182284 * A182286 A182287 A182288

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 23 2012

STATUS

approved

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Last modified May 18 23:56 EDT 2021. Contains 344009 sequences. (Running on oeis4.)