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A176480
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Triangle: let b(n) = 3*b(n - 1) - 2*b(n - 2) + b(n - 3), then T(n,m) = b(n) - b(m) - b(n - m) + 1.
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0
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1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 9, 11, 9, 1, 1, 21, 28, 28, 21, 1, 1, 49, 68, 73, 68, 49, 1, 1, 114, 161, 178, 178, 161, 114, 1, 1, 265, 377, 422, 434, 422, 377, 265, 1, 1, 616, 879, 989, 1029, 1029, 989, 879, 616, 1, 1, 1432, 2046, 2307, 2412, 2440, 2412, 2307, 2046
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listen;
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OFFSET
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0,5
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LINKS
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 4, 4, 1},
{1, 9, 11, 9, 1},
{1, 21, 28, 28, 21, 1},
{1, 49, 68, 73, 68, 49, 1},
{1, 114, 161, 178, 178, 161, 114, 1},
{1, 265, 377, 422, 434, 422, 377, 265, 1},
{1, 616, 879, 989, 1029, 1029, 989, 879, 616, 1},
{1, 1432, 2046, 2307, 2412, 2440, 2412, 2307, 2046, 1432, 1}
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MATHEMATICA
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b[0] := 0; b[1] := 1; b[2] := 3;
b[n_] := b[n] = 3*b[n - 1] - 2*b[n - 2] + b[n - 3];
t[n_, m_] := t[n, m] = b[n] - b[m] - b[n - m] + 1;
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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STATUS
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approved
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