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%I #4 Jul 10 2023 19:25:01
%S 0,96,189,453,969,1496,3020,6020,9089,17969,35453,53340,105096,207000,
%T 311253,612909,1206849,1814480,3572660,7034396,10575929,20823353,
%U 40999829,61641396,121367760,238964880,359272749,707383509,1392789753
%N Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+151)^2 = y^2.
%C Corresponding values y of solutions (x, y) are in A161483.
%C lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C lim_{n -> infinity} a(n)/a(n-1) = (187+78*sqrt(2))/151 for n mod 3 = {1, 2}.
%C lim_{n -> infinity} a(n)/a(n-1) = (24723+6758*sqrt(2))/151^2 for n mod 3 = 0.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).
%F a(n) = 6*a(n-3)-a(n-6)+302 for n > 6; a(1)=0, a(2)=96, a(3)=189, a(4)=453, a(5)=969, a(6)=1496.
%F G.f.: x*(96+93*x+264*x^2-60*x^3-31*x^4-60*x^5) / ((1-x)*(1-6*x^3+x^6)).
%F a(3*k+1) = 151*A001652(k) for k >= 0.
%t LinearRecurrence[{1,0,6,-6,0,-1,1},{0,96,189,453,969,1496,3020},30] (* _Harvey P. Dale_, Jul 10 2023 *)
%o (PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+302*n+22801), print1(n, ",")))}
%Y Cf. A161483, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A161484 (decimal expansion of (187+78*sqrt(2))/151), A161485 (decimal expansion of (24723+6758*sqrt(2))/151^2).
%K nonn
%O 1,2
%A _Klaus Brockhaus_, Jun 13 2009
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