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A112531 Triangle read by rows which lists compositions having at least one part equal to 1.

%I A112531 #27 May 19 2014 14:48:13
%S A112531 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 A112531 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 A112531 20,20,5,15,6,1
%N A112531 Triangle read by rows which lists compositions having at least one part equal to 1.
%C A112531 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 A112531 Row sums give A112532; which are the first differences of A047970.
%C A112531 Row lengths give A011782.
%e A112531 The partitions (see A241596) begin 1 2 11 3 22 21 111 4 33 32 222 31 221 211 1111 ...
%e A112531 After omitting partitions with no part equal to 1, we have
%e A112531 1 11 21 111 31 221 211 1111 ...
%e A112531 which give rise to 1 1 2 1 2 3 3 1 ... compositions.
%e A112531 The resulting triangle of compositions begins:
%e A112531 1;
%e A112531 1;
%e A112531 2, 1;
%e A112531 2, 3, 3, 1;
%e A112531 2, 3, 6, 4, 3, 6, 4, 1;
%e A112531 2, 3, 6, 4, 6, 12, 12, 5, 3, 6, 12, 10, 4, 10, 5, 1;
%e A112531 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 A112531 ...
%Y A112531 Cf. A000079, A011782, A047970, A089246, A112532, A241596, A242628.
%K A112531 nonn,tabf
%O A112531 1,3
%A A112531 _Alford Arnold_, Sep 10 2005
%E A112531 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_.