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%I #27 May 19 2014 14:48:13
%S 1,1,2,1,2,3,3,1,2,3,6,4,3,6,4,1,2,3,6,4,6,12,12,5,3,6,12,10,4,10,5,1,
%T 2,3,6,4,6,12,12,5,6,12,24,20,12,30,20,6,3,6,12,10,12,30,30,15,4,10,
%U 20,20,5,15,6,1
%N Triangle read by rows which lists compositions having at least one part equal to 1.
%C Consider partitions listed in the order given by A241596 and A242628. Omit any partition not containing 1 as a part. Write down the number of compositions (= ordered partitions) corresponding to this partition.
%C Row sums give A112532; which are the first differences of A047970.
%C Row lengths give A011782.
%e The partitions (see A241596) begin 1 2 11 3 22 21 111 4 33 32 222 31 221 211 1111 ...
%e After omitting partitions with no part equal to 1, we have
%e 1 11 21 111 31 221 211 1111 ...
%e which give rise to 1 1 2 1 2 3 3 1 ... compositions.
%e The resulting triangle of compositions begins:
%e 1;
%e 1;
%e 2, 1;
%e 2, 3, 3, 1;
%e 2, 3, 6, 4, 3, 6, 4, 1;
%e 2, 3, 6, 4, 6, 12, 12, 5, 3, 6, 12, 10, 4, 10, 5, 1;
%e 2, 3, 6, 4, 6, 12, 12, 5, 6, 12, 24, 20, 12, 30, 20, 6, 3, 6, 12, 10, 12, 30, 30, 15, 4, 10, 20, 20, 5, 15, 6, 1;
%e ...
%Y Cf. A000079, A011782, A047970, A089246, A112532, A241596, A242628.
%K nonn,tabf
%O 1,3
%A _Alford Arnold_, Sep 10 2005
%E Edited by _N. J. A. Sloane_, May 19 2014 based on postings to the Sequence Fans Mailing List by _Peter Luschny_, Jonas Wallgren, _Arie Groeneveld_, and _Franklin T. Adams-Watters_.
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