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.

5, 19, 21, 73, 91, 93, 275, 383, 407, 409, 1075, 1639, 1821, 1851, 1853, 4133, 6881, 8019, 8295, 8331, 8333, 16249, 29155, 35507, 37531, 37921, 37963, 37965, 63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265, 249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557

Offset: 1

Author

Scott R. Shannon, Oct 11 2020

Keywords

• nonn
• tabl

Examples

			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.
The table begins:
5;
19, 21;
73, 91, 93;
275, 383, 407, 409;
1075, 1639, 1821, 1851, 1853;
4133, 6881, 8019, 8295, 8331, 8333;
16249, 29155, 35507, 37531, 37921, 37963, 37965;
63293, 122491, 155525, 168399, 171691, 172215, 172263, 172265;
249445, 519351, 683711, 758183, 781811, 786823, 787501, 787555, 787557;
		

Crossrefs

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

Formula

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