%I #17 Apr 07 2020 10:38:14
%S 1,1,11,191,11346,2002405,1112939654,1878223479450
%N Number of self-avoiding closed paths in the n X n grid graph which pass through all vertices on four (left, right, upper, lower) sides of the graph.
%C a(11) = 152567999801505122456.
%e a(2) = 1;
%e +--+
%e | |
%e +--+
%e a(3) = 1;
%e +--+--+
%e | |
%e + +
%e | |
%e +--+--+
%e a(4) = 11;
%e +--+--+--+ +--+--+--+ +--+--+--+
%e | | | | | |
%e +--*--* + +--* *--+ +--* +
%e | | | | | |
%e +--*--* + +--* *--+ +--* +
%e | | | | | |
%e +--+--+--+ +--+--+--+ +--+--+--+
%e +--+--+--+ +--+--+--+ +--+--+--+
%e | | | | | |
%e + *--*--+ + *--* + + *--+
%e | | | | | | | |
%e + *--*--+ + * * + + *--+
%e | | | | | | | |
%e +--+--+--+ +--+ +--+ +--+--+--+
%e +--+--+--+ +--+--+--+ +--+ +--+
%e | | | | | | | |
%e + + + + + *--* +
%e | | | | | |
%e + *--* + + + + *--* +
%e | | | | | | | | | |
%e +--+ +--+ +--+--+--+ +--+ +--+
%e +--+ +--+ +--+ +--+
%e | | | | | | | |
%e + *--* + + * * +
%e | | | | | |
%e + + + *--* +
%e | | | |
%e +--+--+--+ +--+--+--+
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o import graphillion.tutorial as tl
%o def A333759(n):
%o universe = tl.grid(n - 1, n - 1)
%o GraphSet.set_universe(universe)
%o cycles = GraphSet.cycles()
%o points = [i for i in range(1, n * n + 1) if i % n < 2 or ((i - 1) // n + 1) % n < 2]
%o for i in points:
%o cycles = cycles.including(i)
%o return cycles.len()
%o print([A333759(n) for n in range(2, 10)])
%Y Main diagonal of A333758.
%Y Cf. A333466.
%K nonn,more
%O 2,3
%A _Seiichi Manyama_, Apr 04 2020