A238348 Triangle T(n,k) read by rows: T(n,k) is the number of compositions of n where the k-th part is the last occurrence of a smallest part, n>=1, 1<=k<=n.

1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 4, 4, 4, 3, 1, 5, 7, 8, 7, 4, 1, 8, 11, 14, 14, 11, 5, 1, 12, 18, 23, 27, 25, 16, 6, 1, 19, 27, 39, 49, 51, 41, 22, 7, 1, 28, 44, 64, 85, 98, 92, 63, 29, 8, 1, 45, 69, 103, 144, 180, 189, 155, 92, 37, 9, 1, 70, 109, 166, 241, 319, 366, 344, 247, 129, 46, 10, 1

Offset: 1

Author

Joerg Arndt and Alois P. Heinz, Feb 25 2014

Keywords

• nonn
• tabl

Comments

Column k=1 is A079501.

Row sums are A011782.

Examples

			Triangle starts:
01:  1,
02:  1, 1,
03:  2, 1, 1,
04:  2, 3, 2, 1,
05:  4, 4, 4, 3, 1,
06:  5, 7, 8, 7, 4, 1,
07:  8, 11, 14, 14, 11, 5, 1,
08:  12, 18, 23, 27, 25, 16, 6, 1,
09:  19, 27, 39, 49, 51, 41, 22, 7, 1,
10:  28, 44, 64, 85, 98, 92, 63, 29, 8, 1,
11:  45, 69, 103, 144, 180, 189, 155, 92, 37, 9, 1,
12:  70, 109, 166, 241, 319, 366, 344, 247, 129, 46, 10, 1,
13:  110, 172, 267, 398, 551, 679, 709, 591, 376, 175, 56, 11, 1,
...
		

Links

• Joerg Arndt, Table of n, a(n) for n = 1..465 (rows 1..30, flattened)