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1, 2, 6, 3, 9, 18, 4, 12, 24, 40, 5, 15, 30, 50, 75, 6, 18, 36, 60, 90, 126, 7, 21, 42, 70, 105, 147, 196, 8, 24, 48, 80, 120, 168, 224, 288, 9, 27, 54, 90, 135, 189, 252, 324, 405, 10, 30, 60, 100, 150, 210, 280, 360, 450, 550
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n, k) = n * binomial(k+1, 2).
Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = (1/4)*(4*n - 3*floor((n+1)/2) + 3)*binomial(2 + floor((n+1)/2), 3).
T(2*n-2, n-1) = A011379(n-1), n >= 2. (End)
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EXAMPLE
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First few rows of the triangle =
1;
2, 6;
3, 9, 18;
4, 12, 24, 40;
5, 15, 30, 50, 75;
6, 18, 36, 60, 90, 126;
7, 21, 42, 70, 105, 147, 196;
...
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MATHEMATICA
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Table[n*Binomial[k+1, 2], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Jul 12 2022 *)
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PROG
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(Magma) [n*Binomial(k+1, 2): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 12 2022
(SageMath) flatten([[n*binomial(k+1, 2) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Jul 12 2022
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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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