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%I #17 Feb 01 2021 00:19:00
%S 6,24,6,72,30,6,168,144,30,6,456,624,150,30,6,1032,2520,720,150,30,6,
%T 2712,9360,3408,726,150,30,6,5784,34008,15432,3528,726,150,30,6,14640,
%U 120960,68088,16776,3534,726,150,30,6,29760,430656,289128,79320,16920,3534,726,150,30,6
%N Table read by antidiagonals: T(h,n) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2h X 2h X 2h where the walk starts at the center of the box.
%F For n <= h, T(h,n) = A001412(n).
%F Row 1 = T(1,n) = A337021(n).
%F For n >= (2h+1)^3, T(h,n) = 0 as the walk contains more steps than there are available lattice points in the 2h X 2h X 2h box.
%e T(1,2) = 24 as after a step in one of the six axial directions the walk must turn along the face of the box; this eliminates the 2-step straight walk in all directions, so the total number of walks is 6*5-6 = 24.
%e .
%e The table begins:
%e .
%e 6 24 72 168 456 1032 2712 5784 14640 29760 71136 133344 291696..
%e 6 30 144 624 2520 9360 34008 120960 430656 1511856 5340312 18587208 65176416..
%e 6 30 150 720 3408 15432 68088 289128 1205976 4920528 19985928 80066136 321160728..
%e 6 30 150 726 3528 16776 79320 366960 1677864 7516992 33312456 145379760 630249720..
%e 6 30 150 726 3534 16920 81216 385224 1822584 8518920 39588480 181800312 829567656..
%e 6 30 150 726 3534 16926 81384 387768 1850376 8765304 41478144 194837136 912538512..
%e 6 30 150 726 3534 16926 81390 387960 1853664 8805504 41872944 198158520 937459176..
%e 6 30 150 726 3534 16926 81390 387966 1853880 8809632 41928816 198761160 942984312..
%e 6 30 150 726 3534 16926 81390 387966 1853886 8809872 41933880 198836352 943868424..
%e 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934144 198842448 943966968..
%e 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934150 198842736 943974192..
%e 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934150 198842742 943974504..
%e 6 30 150 726 3534 16926 81390 387966 1853886 8809878 41934150 198842742 943974510..
%Y Cf. A001412 (h->infinity), A337021 (h=1), A337031 (start at center of face), A337035 (start as corner of box), A336862 (start at middle of edge), A116904, A039648.
%K nonn,walk,tabl
%O 1,1
%A _Scott R. Shannon_, Aug 11 2020