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A144650
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Triangle read by rows where T(m,n) = 2m*n + m + n + 1.
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6
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5, 8, 13, 11, 18, 25, 14, 23, 32, 41, 17, 28, 39, 50, 61, 20, 33, 46, 59, 72, 85, 23, 38, 53, 68, 83, 98, 113, 26, 43, 60, 77, 94, 111, 128, 145, 29, 48, 67, 86, 105, 124, 143, 162, 181, 32, 53, 74, 95, 116, 137, 158, 179, 200, 221, 35, 58, 81, 104, 127, 150, 173, 196, 219, 242, 265
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Sum_{n=1..m} T(m, n) = m*(2*m+3)*(m+1)/2 = A160378(n+1) (row sums). - R. J. Mathar, Jan 15 2009, Jan 05 2011
T(n, n-3) = (-1)*A147973(n+2), n >= 4.
Sum_{k=1..n} (-1)^k*T(n, k) = (-1)^n*A007742(floor((n+1)/2)).
G.f.: x*y*(5 - 2*x - 2*x*y - 2*x^2*y + x^2*y^2)/((1-x)^2*(1-x*y)^3). (End)
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EXAMPLE
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Triangle begins:
5;
8, 13;
11, 18, 25;
14, 23, 32, 41;
17, 28, 39, 50, 61;
20, 33, 46, 59, 72, 85;
23, 38, 53, 68, 83, 98, 113;
26, 43, 60, 77, 94, 111, 128, 145;
29, 48, 67, 86, 105, 124, 143, 162, 181;
32, 53, 74, 95, 116, 137, 158, 179, 200, 221; etc.
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MATHEMATICA
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T[n_, k_]:= 2 n*k + n + k + 1; Table[T[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)
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PROG
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(Magma) [2*n*k + n + k + 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
(SageMath) flatten([[2*n*k+n+k+1 for k in range(1, n+1)] for n in range(1, 13)]) # G. C. Greubel, Oct 14 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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