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A333513
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Square array T(n,k), n >= 2, k >= 2, read by antidiagonals, where T(n,k) is the number of self-avoiding closed paths on an n X k grid which pass through four corners ((0,0), (0,k-1), (n-1,k-1), (n-1,0)).
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7
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1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 7, 11, 7, 1, 1, 17, 49, 49, 17, 1, 1, 41, 229, 373, 229, 41, 1, 1, 99, 1081, 3105, 3105, 1081, 99, 1, 1, 239, 5123, 26515, 44930, 26515, 5123, 239, 1, 1, 577, 24323, 227441, 674292, 674292, 227441, 24323, 577, 1
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OFFSET
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2,8
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LINKS
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Seiichi Manyama, Antidiagonals n = 2..15, flattened
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FORMULA
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T(n,k) = T(k,n).
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EXAMPLE
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Square array T(n,k) begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 3, 7, 17, 41, ...
1, 3, 11, 49, 229, 1081, ...
1, 7, 49, 373, 3105, 26515, ...
1, 17, 229, 3105, 44930, 674292, ...
1, 41, 1081, 26515, 674292, 17720400, ...
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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()
print([A333513(j + 2, i - j + 2) for i in range(11 - 1) for j in range(i + 1)])
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CROSSREFS
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Column k=2-7 give: A000012, A001333(n-2), A333514, A333515, A358712, A358713.
Main diagonal gives A333466.
Cf. A333758.
Sequence in context: A075772 A142157 A119608 * A196646 A196601 A196578
Adjacent sequences: A333510 A333511 A333512 * A333514 A333515 A333516
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KEYWORD
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nonn,tabl
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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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