A238347 Triangle T(n,k) read by rows: T(n,k) is the number of compositions of n where the k-th part is the first occurrence of a smallest part, n>=1, 1<=k<=n.

1, 2, 0, 3, 1, 0, 6, 2, 0, 0, 10, 5, 1, 0, 0, 20, 9, 3, 0, 0, 0, 37, 19, 7, 1, 0, 0, 0, 72, 36, 16, 4, 0, 0, 0, 0, 140, 71, 33, 11, 1, 0, 0, 0, 0, 275, 139, 67, 26, 5, 0, 0, 0, 0, 0, 540, 274, 135, 58, 16, 1, 0, 0, 0, 0, 0, 1069, 539, 269, 123, 42, 6, 0, 0, 0, 0, 0, 0, 2118, 1068, 534, 254, 99, 22, 1, 0

Offset: 1

Author

Joerg Arndt and Alois P. Heinz, Feb 25 2014

Keywords

• nonn
• tabl

Comments

Column k=0 is A238351. Column k=1 is A171682.

Row sums are A011782.

Examples

			Triangle starts:
01:  1,
02:  2, 0,
03:  3, 1, 0,
04:  6, 2, 0, 0,
05:  10, 5, 1, 0, 0,
06:  20, 9, 3, 0, 0, 0,
07:  37, 19, 7, 1, 0, 0, 0,
08:  72, 36, 16, 4, 0, 0, 0, 0,
09:  140, 71, 33, 11, 1, 0, 0, 0, 0,
10:  275, 139, 67, 26, 5, 0, 0, 0, 0, 0,
11:  540, 274, 135, 58, 16, 1, 0, 0, 0, 0, 0,
12:  1069, 539, 269, 123, 42, 6, 0, 0, 0, 0, 0, 0,
13:  2118, 1068, 534, 254, 99, 22, 1, 0, 0, 0, 0, 0, 0,
14:  4206, 2117, 1062, 516, 220, 64, 7, 0, 0, 0, 0, 0, 0, 0,
15:  8365, 4205, 2111, 1040, 470, 163, 29, 1, 0, 0, 0, 0, 0, 0, 0,
...
		

Links

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