A125104 Triangle read by rows counting compositions (ordered partitions) by minimal part size.

1, 1, 1, 1, 0, 3, 1, 0, 1, 6, 1, 0, 0, 2, 13, 1, 0, 0, 1, 3, 27, 1, 0, 0, 0, 2, 5, 56, 1, 0, 0, 0, 1, 2, 9, 115, 1, 0, 0, 0, 0, 2, 3, 15, 235, 1, 0, 0, 0, 0, 1, 2, 5, 25, 478, 1, 0, 0, 0, 0, 0, 2, 2, 8, 42, 969, 1, 0, 0, 0, 0, 0, 1, 2, 3, 12, 70, 1959, 1, 0, 0, 0, 0, 0, 0, 2, 2, 5, 18, 116, 3952, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 8, 27, 192, 7959, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 11, 41, 317, 16007

Offset

0,6

Comments

The diagonals of this array can be generated from Table A099238 as follows: A000079 - A000045 = [1, 2, 4, 8, 16, 32, ...] - [0, 1, 1, 2, 3, 5, ...] = [1, 1, 3, 6, 13, 27, ...] = A099036, A000045 - A000930, A000930 - A003269, A003269 - A003520, etc.

Links

Table of n, a(n) for n=0..119.

Example

Row 4 of the array is (1, 0, 1, 6) because there are six compositions with minimum part of size one: 1111, 31, 13, 211, 121, 112; one of size two: 22; none of size three; and 1 of size four: 4.
Triangle (after 45-degree counterclockwise rotation) begins:
1 1 3 6 13 27 56 115 235 478 969 1959 3952 7959
.1 0 1 2 3 5 9 15 25 42 70 116 192
..1 0 0 1 2 2 3 5 8 12 18 27
...1 0 0 0 1 2 2 2 3 5 8
....1 0 0 0 0 1 2 2 2 2
.....1 0 0 0 0 0 1 2 2
......1 0 0 0 0 0 0 1
.......1 0 0 0 0 0 0
........1 0 0 0 0 0

Crossrefs

Cf. A000079, A000045, A000930, A003269, A003520, A099036, A099238.

Cf. A105147.

Sequence in context: A119271 A364310 A323222 * A098157 A293617 A165253

Adjacent sequences: A125101 A125102 A125103 * A125105 A125106 A125107

Keyword

easy,nonn,tabl

Author

Alford Arnold, Nov 28 2006, corrected Nov 28 2006

Extensions

Edited by N. J. A. Sloane, Dec 21 2006

More terms from Vladeta Jovovic, Jul 10 2007

Status

approved