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A353091
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Irregular triangle read by rows: T(n, k) is the number of n-step closed walks on the hexagonal lattice having algebraic area k.
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0
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1, 6, 0, 6, 66, 0, 12, 0, 150, 0, 30, 1020, 0, 420, 0, 84, 0, 6, 0, 3444, 0, 1302, 0, 252, 0, 42, 19890, 0, 11952, 0, 4284, 0, 984, 0, 216, 0, 24, 0, 82062, 0, 42972, 0, 14814, 0, 4248, 0, 990, 0, 216, 0, 18, 449976, 0, 327420, 0, 158970, 0, 57180, 0, 18780, 0, 5190, 0, 1350, 0, 270, 0, 30
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OFFSET
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0,2
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COMMENTS
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Rows 0 and 2 have 1 element each; row 1 is empty; for n > 2, we have 0 <= k <= A069813(n).
Rows can be extended to negative k with T(n, -k) = T(n, k). Sums of such extended rows give A002898.
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LINKS
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EXAMPLE
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The triangle begins:
[1]
[]
[6]
[0, 6]
[66, 0, 12]
[0, 150, 0, 30]
[1020, 0, 420, 0, 84, 0, 6]
[0, 3444, 0, 1302, 0, 252, 0, 42]
[19890, 0, 11952, 0, 4284, 0, 984, 0, 216, 0, 24]
[0, 82062, 0, 42972, 0, 14814, 0, 4248, 0, 990, 0, 216, 0, 18]
[449976, 0, 327420, 0, 158970, 0, 57180, 0, 18780, 0, 5190, 0, 1350, 0, 270, 0, 30]
...
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CROSSREFS
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For n > 1, row n seems to end with A109047(n).
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KEYWORD
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nonn,tabf,walk
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AUTHOR
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STATUS
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approved
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