A225877 - OEIS

%I #10 Jan 11 2020 10:10:46

%S 1,2,6,28,140,744,4116,23504,137412,818260,4945292,30255240,187009888,

%T 1166065936,7325767920,46326922560,294658864188,1883761686216,

%U 12098003064296,78015400052920,504955502402148,3279315915221192,21361995729759184,139545638718942960

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

%C 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.

%H Felix A. Pahl, <a href="/A225877/b225877.txt">Table of n, a(n) for n = 1..55</a>

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

%t A002931 = Cases[Import["https://oeis.org/A002931/b002931.txt", "Table"], {_, _}][[All, 2]]; a[n_] := n A002931[[n]];

%t a /@ Range[55] (* _Jean-François Alcover_, Jan 11 2020 *)

%K nonn

%O 1,2

%A _Felix A. Pahl_, May 19 2013