A225877 Number of (2n-1)-step self-avoiding paths between two adjacent sites of a 2-dimensional square lattice.

1, 2, 6, 28, 140, 744, 4116, 23504, 137412, 818260, 4945292, 30255240, 187009888, 1166065936, 7325767920, 46326922560, 294658864188, 1883761686216, 12098003064296, 78015400052920, 504955502402148, 3279315915221192, 21361995729759184, 139545638718942960

Offset: 1

Author

Felix A. Pahl, May 19 2013

Keywords

• nonn

Comments

For n > 1, a(n) = A010566(n)/4: every self-avoiding open path from P to an adjacent site Q (except the one for n = 1) can be completed to a self-avoiding closed path by adding an edge from Q back to P, and exactly 1/4 of all closed paths through P contain that edge.

Links

• Felix A. Pahl, Table of n, a(n) for n = 1..55

Programs

Mathematica

A002931 = Cases[Import["https://oeis.org/A002931/b002931.txt", "Table"], {, }][[All, 2]]; a[n_] := n A002931[[n]];
a /@ Range[55] (* Jean-François Alcover, Jan 11 2020 *)

Formula

For n>1, a(n) = n*A002931(n) = A010566(n)/4.