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A083487
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Triangle read by rows: T(n,k) = 2*n*k + n + k (1 <= k <= n).
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9
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4, 7, 12, 10, 17, 24, 13, 22, 31, 40, 16, 27, 38, 49, 60, 19, 32, 45, 58, 71, 84, 22, 37, 52, 67, 82, 97, 112, 25, 42, 59, 76, 93, 110, 127, 144, 28, 47, 66, 85, 104, 123, 142, 161, 180, 31, 52, 73, 94, 115, 136, 157, 178, 199, 220, 34, 57, 80, 103, 126, 149, 172, 195, 218, 241, 264
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OFFSET
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1,1
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COMMENTS
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T(n,k) gives number of edges (of unit length) in a k X n grid.
The values 2*T(n,k)+1 = (2*n+1)*(2*k+1) are nonprime and therefore in A047845.
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LINKS
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FORMULA
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Sum_{k=1..n} (-1)^(k-1)*T(n, k) = A182868((n+1)/2) if n is odd otherwise A182868(n/2) + 1. (End)
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EXAMPLE
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Triangle begins:
4;
7, 12;
10, 17, 24;
13, 22, 31, 40;
16, 27, 38, 49, 60;
19, 32, 45, 58, 71, 84;
22, 37, 52, 67, 82, 97, 112;
25, 42, 59, 76, 93, 110, 127, 144;
28, 47, 66, 85, 104, 123, 142, 161, 180;
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MATHEMATICA
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T[n_, k_]:= 2 n k + n + k; Table[T[n, k], {n, 10}, {k, n}]//Flatten (* Vincenzo Librandi, Jun 01 2014 *)
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PROG
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(Magma) [(2*n*k + n + k): k in [1..n], n in [1..11]]; // Vincenzo Librandi, Jun 01 2014
(Python)
def T(r, c): return 2*r*c + r + c
a = [T(r, c) for r in range(12) for c in range(1, r+1)]
(SageMath) flatten([[2*n*k +n +k for k in range(1, n+1)] for n in range(1, 14)]) # G. C. Greubel, Oct 17 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Jun 09 2003
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EXTENSIONS
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STATUS
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approved
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