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A289156
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Largest area of triangles with integer sides and area = n times perimeter.
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3
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60, 1224, 8436, 34320, 103020, 254040, 546084, 1060896, 1907100, 3224040, 5185620, 8004144, 11934156, 17276280, 24381060, 33652800, 45553404, 60606216, 79399860, 102592080, 130913580, 165171864, 206255076, 255135840
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: 12*x*(5 + 72*x + 166*x^2 + 72*x^3 + 5*x^4) / (1 - x)^6.
a(n) = 4*n*(2*n^2 + 1)*(4*n^2 + 1).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
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EXAMPLE
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For n = 4, a(4) = 34320 means for the largest triangles (a,b,c) = (66,4225,4289), the area is 34320 which is 4 times the perimeter 8580.
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MATHEMATICA
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Table[4 n (2 n^2 + 1) (4 n^2 + 1), {n, 27}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {60, 1224, 8436, 34320, 103020, 254040}, 27] (* or *) Rest@ CoefficientList[Series[12 x (5 + 72 x + 166 x^2 + 72 x^3 + 5 x^4)/(1 - x)^6, {x, 0, 27}], x] (* Michael De Vlieger, Jul 03 2017 *)
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PROG
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(PARI) Vec(12*x*(5 + 72*x + 166*x^2 + 72*x^3 + 5*x^4) / (1 - x)^6 + O(x^30)) \\ Colin Barker, Jun 28 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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