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A332023
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T(n, k) = binomial(n+2, 3) + binomial(k+1, 2) + binomial(k, 1). Triangle read by rows, T(n, k) for 0 <= k <= n.
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2
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0, 1, 3, 4, 6, 9, 10, 12, 15, 19, 20, 22, 25, 29, 34, 35, 37, 40, 44, 49, 55, 56, 58, 61, 65, 70, 76, 83, 84, 86, 89, 93, 98, 104, 111, 119, 120, 122, 125, 129, 134, 140, 147, 155, 164, 165, 167, 170, 174, 179, 185, 192, 200, 209, 219
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OFFSET
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0,3
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COMMENTS
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The sequence increases monotonically.
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LINKS
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FORMULA
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T(n, k) = (1/6)*(3*k^2 + 9*k + n*(n + 1)*(n + 2)).
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EXAMPLE
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The triangle starts:
[0] 0;
[1] 1, 3;
[2] 4, 6, 9;
[3] 10, 12, 15, 19;
[4] 20, 22, 25, 29, 34;
[5] 35, 37, 40, 44, 49, 55;
[6] 56, 58, 61, 65, 70, 76, 83;
[7] 84, 86, 89, 93, 98, 104, 111, 119;
[8] 120, 122, 125, 129, 134, 140, 147, 155, 164;
[9] 165, 167, 170, 174, 179, 185, 192, 200, 209, 219;
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MAPLE
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T := (n, k) -> binomial(n+2, 3) + binomial(k+1, 2) + binomial(k, 1):
seq(seq(T(n, k), k=0..n), n=0..9);
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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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