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

%I A125104 #13 Jan 23 2015 22:34:45
%S A125104 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 A125104 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 A125104 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 A125104 Triangle read by rows counting compositions (ordered partitions) by minimal part size.
%C A125104 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 A125104 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 A125104 Triangle (after 45-degree counterclockwise rotation) begins:
%e A125104 1 1 3 6 13 27 56 115 235 478 969 1959 3952 7959
%e A125104 .1 0 1 2 3 5 9 15 25 42 70 116 192
%e A125104 ..1 0 0 1 2 2 3 5 8 12 18 27
%e A125104 ...1 0 0 0 1 2 2 2 3 5 8
%e A125104 ....1 0 0 0 0 1 2 2 2 2
%e A125104 .....1 0 0 0 0 0 1 2 2
%e A125104 ......1 0 0 0 0 0 0 1
%e A125104 .......1 0 0 0 0 0 0
%e A125104 ........1 0 0 0 0 0
%Y A125104 Cf. A000079, A000045, A000930, A003269, A003520, A099036, A099238.
%Y A125104 Cf. A105147.
%K A125104 easy,nonn,tabl
%O A125104 0,6
%A A125104 _Alford Arnold_, Nov 28 2006, corrected Nov 28 2006
%E A125104 Edited by _N. J. A. Sloane_, Dec 21 2006
%E A125104 More terms from _Vladeta Jovovic_, Jul 10 2007