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
Examples
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;
Links
- Scott R. Shannon, Full data table for n=1 to n=15.
Crossrefs
Formula
For w>=n, T(n,w) = A001412(n).