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A082109
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Third row of number array A082105.
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12
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1, 13, 33, 61, 97, 141, 193, 253, 321, 397, 481, 573, 673, 781, 897, 1021, 1153, 1293, 1441, 1597, 1761, 1933, 2113, 2301, 2497, 2701, 2913, 3133, 3361, 3597, 3841, 4093, 4353, 4621, 4897, 5181, 5473, 5773, 6081, 6397, 6721, 7053, 7393, 7741, 8097, 8461
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OFFSET
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0,2
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COMMENTS
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Define b(n) = A000217(n), the triangular numbers. Using six consecutive terms to create the vertices of a triangle at points (b(n-2), b(n-1)), (b(n), b(n+1)), and (b(n+2), b(n+3)), one fourth the area of these triangles = a(n). - J. M. Bergot, Jul 30 2013
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LINKS
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FORMULA
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a(n) = 4*n^2 + 8*n + 1.
Sum_{n>=0} 1/a(n) = 1/6 - cot(sqrt(3)*Pi/2)*sqrt(3)*Pi/12.
Sum_{n>=0} (-1)^n/a(n) = cosec(sqrt(3)*Pi/2)*sqrt(3)*Pi/12 - 1/6. (End)
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MATHEMATICA
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PROG
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(Magma) [4*n^2+8*n+1: n in [0..60]]; // G. C. Greubel, Dec 22 2022
(SageMath) [4*n^2+8*n+1 for n in range(61)] # G. C. Greubel, Dec 22 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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