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A296795
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Numbers k such that m = 2*k is the middle side in a Heronian triangle with sides m - 11, m, m + 11.
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4
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13, 14, 22, 38, 43, 77, 139, 158, 286, 518, 589, 1067, 1933, 2198, 3982, 7214, 8203, 14861, 26923, 30614, 55462, 100478, 114253, 206987, 374989, 426398, 772486, 1399478, 1591339, 2882957, 5222923, 5938958, 10759342, 19492214, 22164493, 40154411, 72745933
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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 = 363; the corresponding y values are given by A296796.
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LINKS
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FORMULA
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G.f.: (13 + 14*x + 22*x^2 - 14*x^3 - 13*x^4 - 11*x^5) / (1 - 4*x^3 + x^6).
a(n) = 4*a(n-3) - a(n-6) for n>5.
(End)
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EXAMPLE
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The smallest triangle of this type has following sides: 15, 26, 37 has the altitude 12 and is a part of the Pythagorean triangle with sides : 12, 35, 37.
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MATHEMATICA
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CoefficientList[Series[(13 + 14 x + 22 x^2 - 14 x^3 - 13 x^4 - 11 x^5)/(1 - 4 x^3 + x^6), {x, 0, 36}], x] (* Michael De Vlieger, Dec 22 2017 *)
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PROG
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(PARI) Vec((13 + 14*x + 22*x^2 - 14*x^3 - 13*x^4 - 11*x^5) / (1 - 4*x^3 + x^6) + O(x^40)) \\ Colin Barker, Dec 22 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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EXTENSIONS
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STATUS
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approved
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