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A365213
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Triangle T(n, k), n >= 0, k = 0..n, read by rows: let's consider a triangle of initially empty glasses of equal volume, G(n, k), n >= 0, k = 0..n; when water is poured into one of the glasses, say G(n, k), it flows into that glass until it's full, and then the excess overflows equally into G(n+1, k) and G(n+1, k+1); let V(n, k) be the minimum volume of water to be poured into G(0, 0) so as to fill G(n, k) completely; T(n, k) is the denominator of V(n, k) / V(0, 0).
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2
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1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 3, 1, 3, 1, 1, 1, 5, 5, 1, 1, 1, 5, 5, 5, 5, 5, 1, 1, 5, 1, 17, 17, 1, 5, 1, 1, 1, 5, 25, 17, 25, 5, 1, 1, 1, 7, 27, 55, 3, 3, 55, 27, 7, 1, 1, 2, 11, 75, 9, 25, 9, 75, 11, 2, 1, 1, 9, 35, 55, 50, 215, 215, 50, 55, 35, 9, 1
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OFFSET
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0,8
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COMMENTS
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LINKS
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FORMULA
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T(n, k) = T(n, n - k).
T(n, 0) = 1.
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EXAMPLE
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Triangle T(n, k) begins:
1
1 1
1 1 1
1 3 3 1
1 3 1 3 1
1 1 5 5 1 1
1 5 5 5 5 5 1
1 5 1 17 17 1 5 1
1 1 5 25 17 25 5 1 1
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Triangle V(n, k) / V(0, 0) begins:
1
3 3
7 5 7
15 25/3 25/3 15
31 41/3 11 41/3 31
63 22 77/5 77/5 22 63
127 183/5 109/5 93/5 109/5 183/5 127
255 311/5 31 403/17 403/17 31 311/5 255
511 105 226/5 779/25 467/17 779/25 226/5 105 511
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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