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A201075
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Irregular triangle read by rows: number of Schroeder paths of length n and weighted area n^2-k.
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3
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1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 4, 3, 3, 3, 1, 1, 1, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 10, 7, 6, 4, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 14, 17, 22, 25, 27, 31, 34, 34, 33, 31, 28, 21, 14, 10, 5, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 16, 21, 26, 31, 37, 45, 54
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OFFSET
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0,7
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COMMENTS
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0 <= k <= n^2.
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LINKS
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EXAMPLE
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Triangle begins:
1
1 1
1 1 1 2 1
1 1 1 2 3 4 3 3 3 1
1 1 1 2 3 4 5 7 8 9 10 11 10 7 6 4 1
...
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MATHEMATICA
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gf = Expand /@ FixedPoint[1 + x # (1 + q Normal@# /. {x :> q^2 x}) + O[x]^7 &, 0];
Flatten[Reverse[CoefficientList[#, q]] & /@ CoefficientList[gf, x]] (* Andrey Zabolotskiy, Jan 03 2024 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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