A227338 - OEIS

%I #16 Jan 06 2019 06:00:55

%S 1,4,1,12,8,1,44,40,12,1,172,176,84,16,1,772,748,468,144,20,1,3308,

%T 3248,2332,984,220,24,1,14924,14280,11068,5756,1788,312,28,1,64956,

%U 63768,51472,30760,12108,2944,420,32,1,294252,285296,237832,155912,72948,22732,4516

%N Number of n-step self-avoiding walks on cubic lattice ending at point with x = k.

%C The number of walks ending with x = -k is the same as the number ending with x = k.

%H Bert Dobbelaere, <a href="/A227338/b227338.txt">Table of n, a(n) for n = 0..275</a> (terms 0..152 from Joseph Myers)

%H J. L. Martin, <a href="http://dx.doi.org/10.1017/S0305004100036240">The exact enumeration of self-avoiding walks on a lattice</a>, Proc. Camb. Phil. Soc., 58 (1962), 92-101.

%F For n > 0, A001412(n) = T(n,0) + 2 * Sum_{k=1..n} T(n,k). - _Bert Dobbelaere_, Jan 06 2019

%e Initial rows (paths of length 0, 1, 2, ...):

%e 1;

%e 4, 1;

%e 12, 8, 1;

%e 44, 40, 12, 1;

%e ...

%Y Cf. A000759, A000760, A000761, A000762, A001412.

%K nonn,walk,tabl

%O 0,2

%A _Joseph Myers_, Jul 07 2013