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A141429
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Triangle T(n, k) = (k+1)*(n-k+1), read by rows.
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1
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2, 4, 3, 6, 6, 4, 8, 9, 8, 5, 10, 12, 12, 10, 6, 12, 15, 16, 15, 12, 7, 14, 18, 20, 20, 18, 14, 8, 16, 21, 24, 25, 24, 21, 16, 9, 18, 24, 28, 30, 30, 28, 24, 18, 10, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 13
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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T(n, k) = (k+1)*(n-k+1).
Sum_{k=1..n} T(n, k) = A005581(n+1).
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EXAMPLE
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Triangle begins as:
2;
4, 3;
6, 6, 4;
8, 9, 8, 5;
10, 12, 12, 10, 6;
12, 15, 16, 15, 12, 7;
14, 18, 20, 20, 18, 14, 8;
16, 21, 24, 25, 24, 21, 16, 9;
18, 24, 28, 30, 30, 28, 24, 18, 10;
20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
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MAPLE
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(k+1)*(n-k+1) ;
end proc:
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MATHEMATICA
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Table[(k+1)*(n-k+1), {n, 15}, {k, n}]//Flatten
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PROG
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(Magma) [(k+1)*(n-k+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 30 2021
(Sage) flatten([[(k+1)*(n-k+1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 30 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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