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A240837
Partitions as specified by composition into an even number of parts.
4
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
2,4
COMMENTS
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).
EXAMPLE
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
PROG
(PARI) 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))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved