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Triangle read by rows counting compositions (ordered partitions) by minimal part size.
1

%I #13 Jan 23 2015 22:34:45

%S 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,

%T 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,

%U 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

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

%C 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.

%e 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.

%e Triangle (after 45-degree counterclockwise rotation) begins:

%e 1 1 3 6 13 27 56 115 235 478 969 1959 3952 7959

%e .1 0 1 2 3 5 9 15 25 42 70 116 192

%e ..1 0 0 1 2 2 3 5 8 12 18 27

%e ...1 0 0 0 1 2 2 2 3 5 8

%e ....1 0 0 0 0 1 2 2 2 2

%e .....1 0 0 0 0 0 1 2 2

%e ......1 0 0 0 0 0 0 1

%e .......1 0 0 0 0 0 0

%e ........1 0 0 0 0 0

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

%Y Cf. A105147.

%K easy,nonn,tabl

%O 0,6

%A _Alford Arnold_, Nov 28 2006, corrected Nov 28 2006

%E Edited by _N. J. A. Sloane_, Dec 21 2006

%E More terms from _Vladeta Jovovic_, Jul 10 2007