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%I #5 Apr 16 2014 11:10:12
%S 1,1,1,2,1,1,1,2,2,3,2,1,1,1,1,1,2,2,2,3,3,2,2,1,4,3,1,2,1,1,3,2,1,1,
%T 1,1,1,2,2,2,2,3,3,3,2,2,2,1,4,4,3,3,1,2,2,1,1,3,3,2,5,4,1,3,1,1,4,2,
%U 2,1,1,1,3,2,2,4,3,3,2,1
%N Partitions as specified by composition into an even number of parts.
%C The composition specifies the run lengths of the boundary of the Ferrers diagram of the partition.
%C Taking the n-th row as multiple partitions, it consists of those partitions with the first hook size (largest part plus number of parts minus 1) equal to n-1. The number of integers in this n-th row is A001792(n-2), and the row sum is A049611(n-1).
%e For row 11, the 11th row in A240750 is 2,1,1,1. This gives us the Ferrers diagram:
%e * * *
%e * *
%e with boundary 2 horizontal, 1 vertical, 1 horizontal, 1 vertical. This is the diagram for partition [2,2,1].
%e The table starts:
%e []
%e (none)
%e 1
%e 1,1; 2
%e 1,1,1; 2,2; 3; 2,1
%e 1,1,1,1; 2,2,2; 3,3; 2,2,1; 4; 3,1; 2,1,1; 3,2
%o (PARI) evil(n) = local(r=0, m=n); while(m>0, if(m%2==1, r=1-r); m\=2); n*2+r
%o A066099row(n) = {local(v=vector(n), j=0, k=0);
%o while(n>0, k++; if(n%2==1, v[j++]=k; k=0); n\=2);
%o vector(j, i, v[j-i+1])}
%o A240750row(n) = A066099row(evil(n))
%o partpath(v) = {local(j=0,n=0,m=0,r);
%o forstep(k=1,#v,2,n+=v[k];m+=v[k+1]);
%o r=vector(n);
%o forstep(k=1,#v,2,for(i=1,v[k],r[j++]=m);m-=v[k+1]);
%o r}
%o arow(n) = partpath(A240750row(n))
%Y A240750, A066099, A125106.
%K nonn,tabf
%O 2,4
%A _Franklin T. Adams-Watters_, Apr 13 2014
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