

A125104


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


1



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
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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 45degree 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: A121314 A119271 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



