A104707 Triangle read by rows distributing the 1602 multinomials described by A005651(6) related to Young tableau and Kostka numbers.

1, 25, 1, 81, 20, 1, 25, 54, 15, 1, 100, 15, 36, 15, 1, 256, 60, 10, 27, 10, 1, 25, 128, 30, 5, 27, 10, 1, 100, 10, 64, 30, 5, 18, 10, 1, 81, 40, 5, 32, 10, 5, 9, 5, 1, 25, 27, 10, 0, 32, 10, 0, 9, 5, 1, 1, 5, 9, 10, 5, 16, 10, 5, 9, 5, 1

Offset

1,2

Comments

The last row (and the square roots of the first column) is 1 5 9 5 10 16 5 10 9 5 1, which when sorted appears as 1 1 5 5 5 5 9 9 10 10 16 in A003870 and A060240. The 1602 cases are distributed in A036038: 1 6 15 20 30 60 90 120 180 360 720.

References

D. Stanton and D. White, Constructive Combinatorics, 1986, page 83.

Links

Table of n, a(n) for n=1..66.

Example

The triangle is:
1;
25,   1;
81,  20,  1;
25,  54, 15,  1;
100, 15, 36, 15,  1;
256, 60, 10, 27, 10,  1;
25, 128, 30,  5, 27, 10,  1;
100, 10, 64, 30,  5, 18, 10, 1;
81,  40,  5, 32, 10,  5,  9, 5, 1;
25,  27, 10,  0, 32, 10,  0, 9, 5, 1;
1,    5,  9, 10,  5, 16, 10, 5, 9, 5, 1;

Crossrefs

Cf. A000041, A000085, A000142, A003870, A060240, A005651, A036038 and A097522 (a similar triangle distributing the 246 multinomials in A005651(5)).

Cf. A104778.

Sequence in context: A272129 A232989 A040649 * A353700 A040618 A040619

Adjacent sequences: A104704 A104705 A104706 * A104708 A104709 A104710

Keyword

fini,full,nonn,tabl

Author

Alford Arnold, Mar 19 2005

Status

approved