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A293817
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Numbers k such that m=2*k is the middle side in a Heronian triangle with sides m-13, m , m+13.
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2
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13, 14, 19, 26, 37, 62, 91, 134, 229, 338, 499, 854, 1261, 1862, 3187, 4706, 6949, 11894, 17563, 25934, 44389, 65546, 96787, 165662, 244621, 361214, 618259, 912938, 1348069, 2307374, 3407131, 5031062, 8611237, 12715586, 18776179, 32137574, 47455213, 70073654
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OFFSET
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0,1
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COMMENTS
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a(n) gives values of x satisfying 3*x^2 - y^2 = 507; corresponding y values are given by A293846.
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LINKS
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FORMULA
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a(n) = 4*a(n-3)-a(n-6), a(1)= 13, a(2)= 14, a(3)= 19, a(4)= 26, a(5)= 37, a(6)= 62.
G.f.: (13 + 14*x + 19*x^2 - 26*x^3 - 19*x^4 - 14*x^5) / (1 - 4*x^3 + x^6). - Colin Barker, Dec 27 2017
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EXAMPLE
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The smallest triangle of this type with 3 acute angles has the sides: 61, 74, 87.
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MATHEMATICA
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LinearRecurrence[{0, 0, 4, 0, 0, -1}, {13, 14, 19, 26, 37, 62}, 40] (* Harvey P. Dale, Oct 10 2023 *)
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PROG
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(PARI) Vec((13 + 14*x + 19*x^2 - 26*x^3 - 19*x^4 - 14*x^5) / (1 - 4*x^3 + x^6) + O(x^40)) \\ Colin Barker, Dec 27 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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