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A007237
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Number of triangles with integer sides and area = n times perimeter.
(Formerly M3878)
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7
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5, 18, 45, 45, 52, 139, 80, 89, 184, 145, 103, 312, 96, 225, 379, 169, 116, 498, 123, 328, 560, 280, 134, 592, 228, 271, 452, 510, 134, 1036, 144, 280, 639, 339, 597, 1119, 139, 354, 635, 648, 162, 1486, 169, 594, 1215, 354, 186, 1066, 369, 622
(list;
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Ray Chandler, Table of n, a(n) for n = 1..5000 (first 300 terms from Zhining Yang)
Juan V. Savall and Jesus Ferrer, Problem E3408, Amer. Math. Monthly, 99 (1992), 175-176.
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FORMULA
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a(n) = A120062(2n). - Ray Chandler, Jul 27 2017
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EXAMPLE
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For n=2, the a(2)=18 solutions whose area is twice its perimeter: (13,14,15) (12,16,20) (15,15,24) (10,24,26) (11,25,30) (18,20,34) (15,26,37) (14,30,40) (10,35,39) (9,40,41) (12,50,58) (33,34,65) (25,51,74) (9,75,78) (11,90,97) (21,85,104) (19,153,170) (18,289,305).
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PROG
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(PARI) for(k=1, 100, n=0; d=4*k^2; e=3*d; for(b=1, sqrt(e), for(c=2*k, e/b, if(b*c>d && c>=b, f = (b + c)*d / (b * c - d); if(f>=c, a=floor(f); if(a==f, n++))))); print1(n, ", "))
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CROSSREFS
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Sequence in context: A101105 A037140 A321049 * A327842 A000339 A270944
Adjacent sequences: A007234 A007235 A007236 * A007238 A007239 A007240
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe
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EXTENSIONS
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a(16)-a(50) from Les Reid, Jul 06 2010
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STATUS
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approved
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