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A151890
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Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).
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4
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0, 1, 4, 2, 7, 12, 3, 10, 17, 24, 4, 13, 22, 31, 40, 5, 16, 27, 38, 49, 60, 6, 19, 32, 45, 58, 71, 84, 7, 22, 37, 52, 67, 82, 97, 112, 8, 25, 42, 59, 76, 93, 110, 127, 144, 9, 28, 47, 66, 85, 104, 123, 142, 161, 180, 10, 31, 52, 73, 94, 115, 136, 157, 178, 199, 220, 11, 34, 57
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OFFSET
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0,3
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COMMENTS
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T(n,m) is also the edge count of the (n+1) X (m+1) grid graph. - Eric W. Weisstein, Jul 21 2011
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LINKS
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FORMULA
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a(n) = -t^3 + (3/2)*t^2 + (2*n+1/2)*t - n - 1, where t = floor(sqrt(2n+1)+1/2) = round(sqrt(2n+1)). - Ridouane Oudra, Dec 02 2019
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EXAMPLE
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Triangle begins:
0;
1, 4;
2, 7, 12;
3, 10, 17, 24;
4, 13, 22, 31, 40;
5, 16, 27, 38, 49, 60;
The 3 X 2 grid graph has 7 edges, which equals T(2,1).
The 4 X 4 grid graph has 24 edges, which equals T(3,3).
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MAPLE
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T:= (l, c)-> 2*l*c + l + c:
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MATHEMATICA
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Table[2 m n + m + n, {n, 0, 9}, {m, 0, n}]
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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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