A038373
Number of n-step self-avoiding paths on quadrant grid starting at quadrant origin.
Original entry on oeis.org
1, 2, 4, 10, 24, 60, 146, 366, 912, 2302, 5800, 14722, 37368, 95304, 243168, 622518, 1594622, 4094768, 10521384, 27085436, 69768478, 179982688, 464564220, 1200563864, 3104192722, 8034256412, 20803994184, 53915334890, 139785953076, 362681515714, 941361260956, 2444866458524, 6351963691964
Offset: 0
A333651
Triangle T(n,k), n >= 2, 0 <= k <= floor(n^2/2)-2, read by rows, where T(n,k) is the number of 2*(k+2)-cycles in the n X n grid graph which pass through NW corner (0,0).
Original entry on oeis.org
1, 1, 2, 4, 1, 2, 6, 18, 40, 24, 6, 1, 2, 6, 20, 72, 248, 698, 1100, 1096, 662, 206, 1, 2, 6, 20, 74, 298, 1228, 4762, 15984, 40026, 75524, 109150, 121130, 99032, 51964, 11996, 1072, 1, 2, 6, 20, 74, 300, 1300, 5844, 26148, 110942, 427388, 1393796, 3790524, 8648638, 16727776, 27529284, 38120312, 43012614, 37385280, 23166526, 9496426, 2286972, 242764
Offset: 2
T(3,0) = 1;
+--*
| |
*--*
T(3,1) = 2;
+--*--* +--*
| | | |
*--*--* * *
| |
*--*
T(3,2) = 4;
+--*--* +--*--* +--*--* +--*
| | | | | | | |
* * * *--* *--* * * *--*
| | | | | | | |
*--*--* *--* *--* *--*--*
Triangle starts:
===================================================
n\k| 0 1 2 3 4 5 6 ... 10 ... 16
---|-----------------------------------------------
2 | 1;
3 | 1, 2, 4;
4 | 1, 2, 6, 18, 40, 24, 6;
5 | 1, 2, 6, 20, 72, 248, 698, ... , 206;
6 | 1, 2, 6, 20, 74, 298, 1228, .......... , 1072;
7 | 1, 2, 6, 20, 74, 300, 1300, ...
8 | 1, 2, 6, 20, 74, 300, 1302, ...
9 | 1, 2, 6, 20, 74, 300, 1302, ...
-
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333651(n):
universe = tl.grid(n - 1, n - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles().including(1)
return [cycles.len(2 * k).len() for k in range(2, n * n // 2 + 1)]
print([i for n in range(2, 8) for i in A333651(n)])
A039618
Number of 2n-step self-avoiding closed walks on first octant of 3-dimensional cubic lattice, passing through origin.
Original entry on oeis.org
1, 0, 3, 18, 138, 1278, 13410, 154584, 1919352, 25273422, 348989058, 5011939788, 74393974476, 1135821378924
Offset: 0
A038393
Number of 4n-step self-avoiding closed paths on first quadrant grid, passing through origin, symmetric about line y = x.
Original entry on oeis.org
1, 1, 2, 6, 20, 78, 342, 1608, 7966, 41054, 218342, 1191038, 6635164, 37621952, 216557220, 1262829914, 7447921572
Offset: 0
Showing 1-4 of 4 results.