A240750 -id:A240750

Search: a240750 -id:a240750

Displaying 1-1 of 1 result found.

page 1

A240837

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

+10
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

(list; graph; refs; listen; history; text; internal format)

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).

LINKS

Table of n, a(n) for n=2..81.

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; 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]);

arow(n) = partpath(A240750row(n))

CROSSREFS

A240750, A066099, A125106.

KEYWORD

nonn,tabf

AUTHOR

Franklin T. Adams-Watters, Apr 13 2014

STATUS

approved

page 1

Search completed in 0.005 seconds