A338125 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.

6, 28, 30, 124, 148, 150, 516, 692, 724, 726, 2156, 3196, 3492, 3532, 3534, 8804, 14324, 16428, 16876, 16924, 16926, 36388, 64076, 76956, 80700, 81332, 81388, 81390, 148452, 282716, 354740, 380964, 387052, 387900, 387964, 387966, 609812, 1251044, 1631420, 1795212, 1843452, 1852716, 1853812, 1853884, 1853886

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Scott R. Shannon, Full data table for n=1 to n=15.

Formula

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

Example

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.
The table begins:
6;
28,30;
124,148,150;
516,692,724,726;
2156,3196,3492,3532,3534;
8804,14324,16428,16876,16924,16926;
36388,64076,76956,80700,81332,81388,81390;
148452,282716,354740,380964,387052,387900,387964,387966;
609812,1251044,1631420,1795212,1843452,1852716,1853812,1853884,1853886;
2478484,5493804,7431100,8377908,8712892,8795020,8808420,8809796,8809876,8809878;

Crossrefs

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

Sequence in context: A362805 A145551 A356410 * A259917 A083865 A185351

Adjacent sequences: A338122 A338123 A338124 * A338126 A338127 A338128

Keyword

nonn,tabl

Author

Scott R. Shannon, Oct 11 2020

Status

approved