A338127 - OEIS

A338127

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 horizontal planes a distance 2w apart and an orthogonal plane on the y-z axes, where the walk starts at the middle point between the planes on the y-z plane.

%I #18 May 29 2022 21:41:58

%S 5,19,21,73,91,93,275,383,407,409,1075,1639,1821,1851,1853,4133,6881,

%T 8019,8295,8331,8333,16249,29155,35507,37531,37921,37963,37965,63293,

%U 122491,155525,168399,171691,172215,172263,172265,249445,519351,683711,758183,781811,786823,787501,787555,787557

%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 horizontal planes a distance 2w apart and an orthogonal plane on the y-z axes, where the walk starts at the middle point between the planes on the y-z plane.

%F For w>=n, T(n,w) = A116904(n).

%e T(2,1) = 19 as after a step in one of the two directions towards the horizontal planes the walk must turn along the planes; this eliminates the 2-step straight walks in those two directions, so the total number of walks is A116904(2) - 2 = 21 - 2 = 19.

%e The table begins:

%e 5;

%e 19, 21;

%e 73, 91, 93;

%e 275, 383, 407, 409;

%e 1075, 1639, 1821, 1851, 1853;

%e 4133, 6881, 8019, 8295, 8331, 8333;

%e 16249, 29155, 35507, 37531, 37921, 37963, 37965;

%e 63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265;

%e 249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557;

%Y Cf. A116904 (w->infinity), A338125, A001412, A337023, A337400, A039648.

%K nonn,tabl

%O 1,1

%A _Scott R. Shannon_, Oct 11 2020