A240750 -id:A240750 - cp's OEIS frontend

A240837 Partitions as specified by composition into an even number of parts.

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, 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, 2, 1, 1, 1, 3, 2, 2, 4, 3, 3, 2, 1

Offset: 2

Franklin T. Adams-Watters, Apr 13 2014

The composition specifies the run lengths of the boundary of the Ferrers diagram of the partition.

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).

			For row 11, the 11th row in A240750 is 2,1,1,1. This gives us the Ferrers diagram:
* * *
* *
with boundary 2 horizontal, 1 vertical, 1 horizontal, 1 vertical. This is the diagram for partition [2,2,1].
The table starts:
[]
(none)
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

A240750, A066099, A125106.

evil(n) = local(r=0, m=n); while(m>0, if(m%2==1, r=1-r); m\=2); n*2+r
A066099row(n) = {local(v=vector(n), j=0, k=0);
   while(n>0, k++; if(n%2==1, v[j++]=k; k=0); n\=2);
   vector(j, i, v[j-i+1])}
A240750row(n) = A066099row(evil(n))
partpath(v) = {local(j=0,n=0,m=0,r);
   forstep(k=1,#v,2,n+=v[k];m+=v[k+1]);
   r=vector(n);
   forstep(k=1,#v,2,for(i=1,v[k],r[j++]=m);m-=v[k+1]);
   r}
arow(n) = partpath(A240750row(n))

cp's OEIS Frontend

A240837 Partitions as specified by composition into an even number of parts.

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