login
A337403
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 w x w where the walk starts at the tube's edge
2
4, 12, 4, 36, 14, 4, 98, 54, 14, 4, 274, 200, 56, 14, 4, 702, 744, 224, 56, 14, 4, 1854, 2626, 926, 226, 56, 14, 4, 4614, 9186, 3738, 956, 226, 56, 14, 4, 11778, 31122, 15056, 4014, 958, 226, 56, 14, 4, 28914, 105766, 59092, 17074, 4050, 958, 226, 56, 14, 4
OFFSET
1,1
FORMULA
For n <= w, T(w,n) = A259808(n).
EXAMPLE
T(1,2) = 12 as after a step in one of the two directions toward the adjacent tube edge the walk must turn along the side; this eliminates the 2-step straight walk in those two directions, so the total number of walks is 2*3 + 2*4 - 2 = 12.
The table begins:
4 12 36 98 274 702 1854 4614 11778 28914 72394 176310 435346...
4 14 54 200 744 2626 9186 31122 105766 351798 1175726 3859350 12729142...
4 14 56 224 926 3738 15056 59092 230254 881850 3367124 12712194 47952018...
4 14 56 226 956 4014 17074 71774 301578 1251362 5170636 21143094 86148002...
4 14 56 226 958 4050 17464 75060 325064 1400650 6040372 25882446 110668184...
4 14 56 226 958 4052 17506 75584 330070 1440668 6321926 27685144 121407404...
4 14 56 226 958 4052 17508 75632 330748 1447916 6386092 28180426 124857572...
4 14 56 226 958 4052 17508 75634 330802 1448768 6396174 28278426 125681952...
4 14 56 226 958 4052 17508 75634 330804 1448828 6397220 28292004 125825794...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397286 28293264 125843600...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293336 125845094...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293338 125845172...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293338 125845174...
CROSSREFS
Cf. A337400 (start at middle of tube), A337401 (start at center of tube's side) A259808 (w->infinity), A001412, A337023, A259808, A039648.
Sequence in context: A262621 A255289 A348334 * A203031 A336862 A190392
KEYWORD
nonn,walk,tabl
AUTHOR
Scott R. Shannon, Aug 26 2020
STATUS
approved