A058050 - OEIS

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.

%I #13 Jul 14 2024 08:42:35

%S 1,1,1,2,3,6,11,22,43,87,176,357,732,1497,3089,6335,13099,26956,55779,

%T 114904,237734,490096,1013276,2089105,4315487,8894624,18356468,

%U 37813944,77958972,160487953,330533009,679920989,1398944724,2875374720,5910355198,12138248459,24927057132,51151600936

%N 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.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a058/A058050.java">Java program</a> (GitHub)

%e 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.

%K nonn

%O 1,4

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

%E More terms from _Sean A. Irvine_, Jul 21 2022