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

1,2

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

Formula

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

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 *)

Crossrefs

Sequence in context: A065577 A227294 A302336 * A350524 A228842 A218941

Adjacent sequences: A225874 A225875 A225876 * A225878 A225879 A225880

Keyword

nonn

Author

Felix A. Pahl, May 19 2013

Status

approved