Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #19 Mar 26 2020 07:34:01
%S 1,16,95,426,1745,6838,25897,95292,342505,1208392,4201765,14445130,
%T 49221691,166563454,560595853,1878809676,6275993883,20910561068
%N Number of self-avoiding walks in the n X 3 grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side.
%e a(1) = 1;
%e +--*--+
%e a(2) = 16;
%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 A(start, goal, n, k):
%o universe = tl.grid(n - 1, k - 1)
%o GraphSet.set_universe(universe)
%o paths = GraphSet.paths(start, goal)
%o return paths.len()
%o def A333509(n, k):
%o if n == 1: return 1
%o s = 0
%o for i in range(1, n + 1):
%o for j in range(k * n - n + 1, k * n + 1):
%o s += A(i, j, k, n)
%o return s
%o def A333511(n):
%o return A333509(n, 3)
%o print([A333511(n) for n in range(1, 15)])
%Y Column k=3 of A333509.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Mar 25 2020