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A011945
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Areas of almost-equilateral Heronian triangles (integral side lengths m-1, m, m+1 and integral area).
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14
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0, 6, 84, 1170, 16296, 226974, 3161340, 44031786, 613283664, 8541939510, 118973869476, 1657092233154, 23080317394680, 321467351292366, 4477462600698444, 62363009058485850, 868604664218103456, 12098102289994962534, 168504827395711372020, 2346969481249964245746
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OFFSET
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1,2
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COMMENTS
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Corresponding m's are in A016064. Corresponding values of lesser side give A016064.
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LINKS
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FORMULA
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s(n) = floor((a+1)/4)*sqrt(3*(a+3)*(a-1)), where a = A016064(n). - Zak Seidov, Feb 23 2005
a(n) = 14*a(n-1) - a(n-2); a(1) = 0, a(2) = 6.
a(n) = (s/4)*((7 + 4*s)^n - (7 - 4*s)^n), where s = sqrt(3). - Zak Seidov, Apr 02 2014
E.g.f.: 6 - exp(7*x)*(12*cosh(4*sqrt(3)*x) - 7*sqrt(3)*sinh(4*sqrt(3)*x))/2. - Stefano Spezia, Dec 12 2022
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MATHEMATICA
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CoefficientList[Series[6 x/(1 - 14 x + x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{14, -1}, {0, 6}, 20] (* Harvey P. Dale, Jan 24 2015 *)
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CROSSREFS
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Cf. this sequence (areas), A334277 (perimeters).
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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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STATUS
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approved
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