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1, 3, 1, 6, 2, 2, 10, 3, 4, 3, 15, 4, 6, 6, 4, 21, 5, 8, 9, 8, 5, 28, 6, 10, 12, 12, 10, 6, 36, 7, 12, 15, 16, 15, 12, 7, 45, 8, 14, 18, 20, 20, 18, 14, 8, 55, 9, 16, 21, 24, 25, 24, 21, 16, 9, 66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11
(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-k+1)*(k-1), k>1.
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EXAMPLE
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First few rows of the triangle =
1;
3, 1;
6, 2, 2;
10, 3, 4, 3;
15, 4, 6, 6, 4;
21, 5, 8, 9, 8, 5;
28, 6, 10, 12, 12, 10, 6;
36, 7, 12, 15, 16, 15, 12, 7;
45, 8, 14, 18, 20, 20, 18, 14, 8;
55, 9, 16, 21, 24, 25, 24, 21, 16, 9;
66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10;
78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
91, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12;
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MAPLE
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MATHEMATICA
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Table[If[k==1, Binomial[n+1, 2], (n-k+1)*(k-1)], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Apr 01 2021 *)
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PROG
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(Magma) [k eq 1 select Binomial(n+1, 2) else (n-k+1)*(k-1): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 01 2021
(Sage) flatten([[binomial(n+1, 2) if k==1 else (n-k+1)*(k-1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Apr 01 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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