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A333515
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Number of self-avoiding closed paths on an n X 5 grid which pass through four corners ((0,0), (0,4), (n-1,4), (n-1,0)).
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3
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1, 7, 49, 373, 3105, 26515, 227441, 1953099, 16782957, 144262743, 1240194297, 10662034451, 91663230249, 788046822891, 6775004473757, 58246174168047, 500755017859261, 4305100014182879, 37011883913816129, 318199242452585915, 2735628331213604009, 23518793814422304163
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,2
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COMMENTS
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Also number of self-avoiding closed paths on a 5 X n grid which pass through four corners ((0,0), (0,n-1), (4,n-1), (4,0)).
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 2..1000
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EXAMPLE
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a(2) = 1;
+--*--*--*--+
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+--*--*--*--+
a(3) = 7;
+--*--*--*--+ +--*--*--*--+ +--*--*--*--+
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* *--* * * *--*--* * * *--* *
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+--*--* *--+ +--* *--+ +--* *--*--+
+--*--*--*--+ +--*--* *--+ +--* *--*--+
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* * * *--* * * *--* *
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+--*--*--*--+ +--*--*--*--+ +--*--*--*--+
+--* *--+
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* *--*--* *
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+--*--*--*--+
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PROG
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(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333513(n, k):
universe = tl.grid(n - 1, k - 1)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
for i in [1, k, k * (n - 1) + 1, k * n]:
cycles = cycles.including(i)
return cycles.len()
def A333515(n):
return A333513(n, 5)
print([A333515(n) for n in range(2, 25)])
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CROSSREFS
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Column k=5 of A333513.
Sequence in context: A344270 A144820 A344251 * A324353 A349781 A199554
Adjacent sequences: A333512 A333513 A333514 * A333516 A333517 A333518
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Mar 25 2020
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STATUS
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approved
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