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, 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

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