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%I #43 Dec 27 2017 14:55:02
%S 9,24,39,60,105,156,231,396,585,864,1479,2184,3225,5520,8151,12036,
%T 20601,30420,44919,76884,113529,167640,286935,423696,625641,1070856,
%U 1581255,2334924,3996489,5901324,8714055,14915100,22024041,32521296,55663911,82194840
%N Numbers such that k is the altitude of a Heronian triangle with sides m-13, m, m+13.
%C a(n) gives the values of y satifacting 3*x^2 - y^2 = 507; corresponding x values are given by A293817.
%C a(n)/3 is the radius of the inscribed circle.
%H Colin Barker, <a href="/A293846/b293846.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,0,0,-1).
%F a(n) = 4*a(n-3) - a(n-6), a(1)=9, a(2)=24, a(3)=39, a(4)=60, a(5)=105, a(6)=156.
%F G.f.: 3*(3 + 8*x + 13*x^2 + 8*x^3 + 3*x^4) / (1 - 4*x^3 + x^6). - _Colin Barker_, Dec 27 2017
%e If the sides are 15, 28, 41 the triangle has the altitude 9 and is a part of the Pythagorean triangle with the sides 9, 40, 41, so 9 is a term.
%t CoefficientList[ Series[ 3(3x^4 +8x^3 +13x^2 +8x +3)/(x^6 -4x^3 +1), {x, 0, 35}], x] (* or *)
%t LinearRecurrence[{0, 0, 4, 0, 0, -1}, 3 {3, 8, 13, 20, 35, 52}, 36] (* _Robert G. Wilson v_, Dec 27 2017 *)
%o (PARI) Vec(3*(3 + 8*x + 13*x^2 + 8*x^3 + 3*x^4) / (1 - 4*x^3 + x^6) + O(x^40)) \\ _Colin Barker_, Dec 27 2017
%Y Cf. A003500, A005320, A296795, A296796.
%K nonn,easy
%O 0,1
%A _Sture Sjöstedt_, Dec 27 2017
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