A058050 a(n) is the number of different graphs drawn in the following way: you decide for each number k <= n on a pair of positive numbers (x(k),y(k)) such that x(k)+y(k)=k; you draw n points numbered 1 to n; draw two arrows from n, one to x(n) and one to y(n); draw two arrows from each k already reached by an arrow, one to x(k) and one to y(k). The process stops when 1 is the only point reached by an arrow without any arrow leaving it; you can also erase the isolated points.

1, 1, 1, 2, 3, 6, 11, 22, 43, 87, 176, 357, 732, 1497, 3089, 6335, 13099, 26956, 55779, 114904, 237734, 490096, 1013276, 2089105, 4315487, 8894624, 18356468, 37813944, 77958972, 160487953, 330533009, 679920989, 1398944724, 2875374720, 5910355198, 12138248459, 24927057132, 51151600936

Offset

1,4

Links

Table of n, a(n) for n=1..38.

Sean A. Irvine, Java program (GitHub)

Example

a(5)=3: there are two possibilities to cut 5, i.e., (1,4) and (2,3); (1,4) gives two possibilities to draw such a graph because 4 also has two ways of cutting: (2,2) and (1,4); (2,3) gives one possibility; and 2+1=3.

Crossrefs

Sequence in context: A043327 A247968 A005578 * A026418 A063895 A337090

Adjacent sequences: A058047 A058048 A058049 * A058051 A058052 A058053

Keyword

nonn

Author

Mathieu Dupont (mathieudupont(AT)usa.net), Nov 18 2000

Extensions

More terms from Sean A. Irvine, Jul 21 2022

Status

approved