A338125 - OEIS

%I #16 Oct 14 2020 23:16:15

%S 6,28,30,124,148,150,516,692,724,726,2156,3196,3492,3532,3534,8804,

%T 14324,16428,16876,16924,16926,36388,64076,76956,80700,81332,81388,

%U 81390,148452,282716,354740,380964,387052,387900,387964,387966,609812,1251044,1631420,1795212,1843452,1852716,1853812,1853884,1853886

%N Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance 2w apart where the walk starts at the middle point between the planes.

%H Scott R. Shannon, <a href="/A338125/a338125.txt">Full data table for n=1 to n=15</a>.

%F For w>=n, T(n,w) = A001412(n).

%e T(2,1) = 28 as after a step in one of the two directions towards the planes the walk must turn along the plane; this eliminates the 2-step straight walk in those two directions, so the total number of walks is A001412(2) - 2 = 30 - 2 = 28.

%e The table begins:

%e 6;

%e 28,30;

%e 124,148,150;

%e 516,692,724,726;

%e 2156,3196,3492,3532,3534;

%e 8804,14324,16428,16876,16924,16926;

%e 36388,64076,76956,80700,81332,81388,81390;

%e 148452,282716,354740,380964,387052,387900,387964,387966;

%e 609812,1251044,1631420,1795212,1843452,1852716,1853812,1853884,1853886;

%e 2478484,5493804,7431100,8377908,8712892,8795020,8808420,8809796,8809876,8809878;

%Y Cf. A338126 (start on a plane), A001412 (w->infinity), A001412, A337023, A337400, A039648.

%K nonn,tabl

%O 1,1

%A _Scott R. Shannon_, Oct 11 2020