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%I #13 Oct 04 2019 11:46:34
%S 0,276,287,740,759,1587,3059,3120,5687,5796,10580,19136,19491,34440,
%T 35075,62951,112815,114884,202011,205712,368184,658812,670871,1178684,
%U 1200255,2147211,3841115,3911400,6871151,6996876,12516140,22388936,22798587,40049280,40782059,72950687
%N Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x + 529)^2 = y^2.
%C For the generic case x^2 + (x + p^2)^2 = y^2 with p = m^2 - 2 a prime number in A028871, m>=5, (0; p^2) and (2*m^3 + 2*m^2 - 4*m - 4; m^4 + 2*m^3 - 4*m - 4) are solutions.
%H Colin Barker, <a href="/A309998/b309998.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,6,-6,0,0,0,-1,1).
%F a(n) = 6*a(n-5) - a(n-10) + 1058 with a(0) = 0, a(1) = 276, a(2) = 287, a(3) = 740, a(4) = 759, a(5) = 1587, a(6) = 3059, a(7) = 3120, a(8) = 5687, a(9) = 5796.
%F From _Colin Barker_, Aug 27 2019: (Start)
%F G.f.: x^2*(276 + 11*x + 453*x^2 + 19*x^3 + 828*x^4 - 184*x^5 - 5*x^6 - 151*x^7 - 5*x^8 - 184*x^9) / ((1 - x)*(1 - 6*x^5 + x^10)).
%F a(n) = a(n-1) + 6*a(n-5) - 6*a(n-6) - a(n-10) + a(n-11) for n>11.
%F (End)
%t Rest@ CoefficientList[Series[x^2*(276 + 11 x + 453 x^2 + 19 x^3 + 828 x^4 - 184 x^5 - 5 x^6 - 151 x^7 - 5 x^8 - 184 x^9)/((1 - x) (1 - 6 x^5 + x^10)), {x, 0, 36}], x] (* _Michael De Vlieger_, Sep 29 2019 *)
%o (PARI) concat(0, Vec(x^2*(276 + 11*x + 453*x^2 + 19*x^3 + 828*x^4 - 184*x^5 - 5*x^6 - 151*x^7 - 5*x^8 - 184*x^9) / ((1 - x)*(1 - 6*x^5 + x^10)) + O(x^40))) \\ _Colin Barker_, Aug 27 2019
%Y Cf. A207059.
%K nonn,easy
%O 1,2
%A _Mohamed Bouhamida_, Aug 26 2019
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