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A162245
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Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.
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2
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13, 22, 37, 31, 52, 73, 40, 67, 94, 121, 49, 82, 115, 148, 181, 58, 97, 136, 175, 214, 253, 67, 112, 157, 202, 247, 292, 337, 76, 127, 178, 229, 280, 331, 382, 433, 85, 142, 199, 256, 313, 370, 427, 484, 541, 94, 157, 220, 283, 346, 409, 472, 535, 598, 661
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OFFSET
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1,1
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COMMENTS
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If h belongs to the main diagonal of the triangle then 6*h+3 is a square since T(n,n) = (3/2)*(2*n+1)^2-1/2 and 6*T(n,n)+3 = 9*(2*n+1)^2. Also, the first column is A017209 (after 4). - Vincenzo Librandi, Nov 20 2012
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LINKS
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FORMULA
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Row sums: Sum_{m=1..n} T(n,m) = n*(5+6*n^2+15*n)/2. - R. J. Mathar, Jul 26 2009
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EXAMPLE
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Triangle begins:
13;
22, 37;
31, 52, 73;
40, 67, 94, 121;
49, 82, 115, 148, 181;
58, 97, 136, 175, 214, 253;
67, 112, 157, 202, 247, 292, 337;
76, 127, 178, 229, 280, 331, 382, 433; etc.
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MATHEMATICA
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Flatten@Table[6*m*n + 3*m + 3*n + 1, {n, 20}, {m, n}] (* Vincenzo Librandi, Mar 03 2012 *)
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PROG
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(Magma) [6*n*k + 3*n + 3*k + 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012
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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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