Search: id:A102341
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%I A102341
%S A102341 12,120,1848,25080,351780,4890480,68149872,949077360,13219419708,
%T A102341 184120982760,2564481115560,35718589344360,497495864091732,
%U A102341 6929223155685600,96511629630137568,1344233586759971040,18722758603319903340
%N A102341 Areas of 'close-to-equilateral' integer triangles.
%C A102341 A close-to-equilateral integer triangle is defined to be a triangle with 
               integer sides and integer area such that the largest and smallest 
               sides differ in length by unity. The first five close-to-equilateral 
               integer triangles have sides (5, 5, 6), (17, 17, 16), (65, 65, 66), 
               (241, 241, 240) and (901, 901, 902).
%C A102341 Next four terms are: {three sides a<b<c and area} { 46816, 46817, 46817, 
               949077360}, { 174725, 174725, 174726, 13219419708}, { 652080, 652081, 
               652081, 184120982760}, {2433601, 2433601, 2433602, 2564481115560}. 
               Also, the first case {1,1,2,0} - integer triangle with zero area, 
               fully appropriate to definition of 'close-to-equilateral' one, should 
               be added. We have 12 cases and a weak conjecture is that the total 
               number of the 'close-to-equilateral' triangles is finite. - Zak Seidov 
               (zakseidov(AT)yahoo.com), Feb 23 2005
%C A102341 This is an infinite series; two sides are equal in length to the hypotenuse 
               of almost 30-60 triangles and the third side alternates between that 
               length +/- 1. - Dan Sanders (dan(AT)ified.ca), Oct 22 2005
%H A102341 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeronianTriangle.html">Heronian Triangle</a>.
%H A102341 Steven Dutch, <a href="http://www.uwgb.edu/dutchs/RECMATH/rmpowers.htm#almost30">
               Almost 30-60 Triples</a>
%F A102341 (2/3) [A007655(n+2) - (-1)^n*A001353(n+1) ] (conjectured). - Ralf Stephan, 
               May 17 2007
%e A102341 a(2) = 120 because 120 is the area of a triangle with side lengths of 
               16, 17 and 17.
%Y A102341 Sequence in context: A120585 A012565 A012621 this_sequence A009078 A009149 
               A010570
%Y A102341 Adjacent sequences: A102338 A102339 A102340 this_sequence A102342 A102343 
               A102344
%K A102341 easy,nonn
%O A102341 1,1
%A A102341 Johannes Koelman (Joc_Kay(AT)hotmail.com), Feb 20 2005
%E A102341 More terms from Zak Seidov (zakseidov(AT)yahoo.com), Feb 23 2005
%E A102341 More terms from Dan Sanders (dan(AT)ified.ca), Oct 22 2005

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