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A143199
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Triangle read by rows: T(n, m) = if m <= floor(n/2) then (n + 1)*a(m) + n otherwise (n + 1)*a(n - m) + n, where a(m) is A000096.
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0
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-1, -1, -1, -1, 2, -1, -1, 3, 3, -1, -1, 4, 14, 4, -1, -1, 5, 17, 17, 5, -1, -1, 6, 20, 41, 20, 6, -1, -1, 7, 23, 47, 47, 23, 7, -1, -1, 8, 26, 53, 89, 53, 26, 8, -1, -1, 9, 29, 59, 99, 99, 59, 29, 9, -1, -1, 10, 32, 65, 109, 164, 109, 65, 32, 10, -1
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, m) = (n + 1)*(if m <= floor(n/2) then (m - 1)*(m + 2) / 2 else (n - m + 2)*(n - (m + 1)) / 2 fi) + n. - Georg Fischer, Oct 28 2023
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EXAMPLE
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{-1},
{-1, -1},
{-1, 2, -1},
{-1, 3, 3, -1},
{-1, 4, 14, 4, -1},
{-1, 5, 17, 17, 5, -1},
{-1, 6, 20, 41, 20, 6, -1},
{-1, 7, 23, 47, 47, 23, 7, -1},
{-1, 8, 26, 53, 89, 53, 26, 8, -1},
{-1, 9, 29, 59, 99, 99, 59, 29, 9, -1},
{-1, 10, 32, 65, 109, 164, 109, 65, 32, 10, -1}
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MAPLE
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seq(print(seq((n + 1) * (if m <= n/2 then (m - 1) * (m + 2)\
/ 2 else (n - m + 2) * (n - (m + 1)) / 2 fi) + n, m=0..n)), n=0..10); # Georg Fischer, Oct 28 2023
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MATHEMATICA
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a[0] = -1; a[n_] := a[n] = a[n - 1] + n; Table[a[n], {n, 0, 30}]; t[n_, m_] := If[m <= Floor[n/2], (n + 1)*a[m] + n, (n + 1)*a[n - m] + n]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]//Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Definition clarified and offset corrected by Georg Fischer, Oct 28 2023
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STATUS
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approved
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