A337400 Table read by antidiagonals: T(w,n) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a tube of cross section 2w X 2w where the walk starts at the middle of the tube.
6, 26, 6, 98, 30, 6, 330, 146, 30, 6, 1130, 658, 150, 30, 6, 3746, 2858, 722, 150, 30, 6, 12802, 11802, 3450, 726, 150, 30, 6, 42498, 48282, 15930, 3530, 726, 150, 30, 6, 143610, 193714, 72522, 16826, 3534, 726, 150, 30, 6, 472242, 781114, 321794, 80010, 16922, 3534, 726, 150, 30, 6
Offset: 1
Examples
T(1,2) = 26 as after a step in one of the four directions toward the tube's side the walk must turn along the side; this eliminates the 2-step straight walk in those four directions, so the total number of walks is 6*5 - 4 = 26. The table begins: 6 26 98 330 1130 3746 12802 42498 143610 472242 1570714 5110426 16779354... 6 30 146 658 2858 11802 48282 193714 781114 3114890 12508114 49767002 199252346... 6 30 150 722 3450 15930 72522 321794 1415450 6134650 26527690 113725546 487875250... 6 30 150 726 3530 16826 80010 373962 1736538 7946946 36158802 162796866 730521658... 6 30 150 726 3534 16922 81274 386138 1833018 8615906 40370370 187477426 867587114... 6 30 150 726 3534 16926 81386 387834 1851546 8780162 41630146 196172338 923017178... 6 30 150 726 3534 16926 81390 387962 1853738 8806962 41893346 198386594 939630954... 6 30 150 726 3534 16926 81390 387966 1853882 8809714 41930594 198788354 943314378... 6 30 150 726 3534 16926 81390 387966 1853886 8809874 41933970 198838482 943903786... 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934146 198842546 943969482... 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934150 198842738 943974298... 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934150 198842742 943974506... 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934150 198842742 943974510...
Crossrefs
Formula
For n <= w, T(w,n) = A001412(n).