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

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, 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, 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

Offset: 2

Author

Franklin T. Adams-Watters, Apr 12 2014

Keywords

• nonn
• tabf

Comments

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.

Examples

			The table starts:
{}
(none)
11
21,12
31,22,13,1111
41,32,23,2111,14,1211,1121,1112
51,42,33,3111,24,2211,2121,2112,15,1311,1221,1212,1131,1122,1113,111111
		

Crossrefs

Cf. A066099, A240837, A001969, A034008 (compositions in rows), A087447 (parts in rows for n>2).

Programs

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])}
arow(n)=A066099row(evil(n))