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A240750 Table where row n contains all compositions of n into an even number of parts.

%I A240750 #9 Apr 16 2014 11:09:47
%S A240750 1,1,2,1,1,2,3,1,2,2,1,3,1,1,1,1,4,1,3,2,2,3,2,1,1,1,1,4,1,2,1,1,1,1,
%T A240750 2,1,1,1,1,2,5,1,4,2,3,3,3,1,1,1,2,4,2,2,1,1,2,1,2,1,2,1,1,2,1,5,1,3,
%U A240750 1,1,1,2,2,1,1,2,1,2,1,1,3,1,1,1,2,2,1,1,1,3,1,1,1,1,1,1
%N A240750 Table where row n contains all compositions of n into an even number of parts.
%C A240750 Can also be regarded as a table where row n is the n-th composition into an even number of parts, sorted by sum of composition and then reverse lexicographically.
%e A240750 The table starts:
%e A240750 {}
%e A240750 (none)
%e A240750 11
%e A240750 21,12
%e A240750 31,22,13,1111
%e A240750 41,32,23,2111,14,1211,1121,1112
%e A240750 51,42,33,3111,24,2211,2121,2112,15,1311,1221,1212,1131,1122,1113,111111
%o A240750 (PARI) evil(n) = local(r=0,m=n);while(m>0,if(m%2==1,r=1-r);m\=2);n*2+r
%o A240750 A066099row(n) = {local(v=vector(n), j=0, k=0);
%o A240750    while(n>0, k++; if(n%2==1, v[j++]=k; k=0); n\=2);
%o A240750    vector(j, i, v[j-i+1])}
%o A240750 arow(n)=A066099row(evil(n))
%Y A240750 Cf. A066099, A240837, A001969, A034008 (compositions in rows), A087447 (parts in rows for n>2).
%K A240750 nonn,tabf
%O A240750 2,3
%A A240750 _Franklin T. Adams-Watters_, Apr 12 2014