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PROG
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(Python)
# Using graphillion
from graphillion import GraphSet
def make_nXk_king_graph(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))
if i > 1:
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
def A(start, goal, n, k):
universe = make_nXk_king_graph(n, k)
GraphSet.set_universe(universe)
paths = GraphSet.paths(start, goal)
return paths.len()
def A307026(n, k):
m = k * n
s = 0
for i in range(1, m):
for j in range(i + 1, m + 1):
s += A(i, j, n, k)
return s
def A339751(n):
return A307026(n, 3)
print([A339751(n) for n in range(1, 21)])
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