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A339960
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Number of Hamiltonian circuits within parallelograms of size 8 X n on the triangular lattice.
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2
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1, 1676, 183521, 20842802, 3061629439, 418172485806, 56203566442908, 7621726574570613, 1033232532941136255, 139934009951521872490, 18955155770535463735959, 2567688102114635009977537, 347811042296785583958285788, 47113523803568895604053871759, 6381875340326645360658645942215
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listen;
history;
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OFFSET
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2,2
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LINKS
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PROG
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(Python)
# Using graphillion
from graphillion import GraphSet
def make_T_nk(n, k):
grids = []
for i in range(1, k + 1):
for j in range(1, n):
grids.append((i + (j - 1) * k, i + j * k))
if i < k:
grids.append((i + (j - 1) * k, i + j * k + 1))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
return grids
universe = make_T_nk(n, k)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles(is_hamilton=True)
return cycles.len()
print([A339960(n) for n in range(2, 8)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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