|
| |
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
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
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
