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Search: id:A011945
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| A011945 |
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Area of triangles with integral side lengths m-1, m, m+1 and integral area. |
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+0
7
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| 0, 6, 84, 1170, 16296, 226974, 3161340, 44031786, 613283664, 8541939510, 118973869476, 1657092233154, 23080317394680, 321467351292366, 4477462600698444, 62363009058485850
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OFFSET
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1,2
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COMMENT
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Corresponding m's are in A016064. Corresponding values of lesser side give A016064.
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REFERENCES
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E. K. Lloyd "The standard deviation of 1, 2, .., n, Pell's equation and rational triangles", preprint.
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LINKS
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Tanya Khovanova, Recursive Sequences
P. Yiu, "Heron triangles with consecutive sides" in 'Recreational Mathematics' Chap.9.3 pp. 80/360
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FORMULA
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s(n)=[(a+1)/4]*sqrt[3(3+a)(a-1)], where a=A016064(n). - Zak Seidov (zakseidov(AT)yahoo.com), Feb 23 2005
a(n) = 14*a(n-1)-a(n-2); a(1) = 0, a(2) = 6.
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CROSSREFS
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Equals 6 * A007655(n+1).
Cf. A003500, A102341, A103974, A103975, A016064.
Sequence in context: A054605 A119576 A098982 this_sequence A113888 A128575 A014062
Adjacent sequences: A011942 A011943 A011944 this_sequence A011946 A011947 A011948
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KEYWORD
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nonn,easy
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AUTHOR
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E. K. Lloyd
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EXTENSIONS
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Entry revised by njas, Feb 03 2007
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