This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159701 #12 Sep 08 2022 08:45:44
%S A159701 925,967,1013,4537,4835,5153,26297,28043,29905,153245,163423,174277,
%T A159701 893173,952495,1015757,5205793,5551547,5920265,30341585,32356787,
%U A159701 34505833,176843717,188589175,201114733,1030720717,1099178263
%N A159701 Positive numbers y such that y^2 is of the form x^2+(x+967)^2 with integer x.
%C A159701 (-43, a(1)) and (A130017(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+967)^2 = y^2.
%C A159701 Lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A159701 Lim_{n -> infinity} a(n)/a(n-1) = (969+44*sqrt(2))/967 for n mod 3 = {0, 2}.
%C A159701 Lim_{n -> infinity} a(n)/a(n-1) = (2487411+1629850*sqrt(2))/967^2 for n mod 3 = 1.
%H A159701 G. C. Greubel, <a href="/A159701/b159701.txt">Table of n, a(n) for n = 1..3895</a>
%H A159701 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,6,0,0,-1).
%F A159701 a(n) = 6*a(n-3) - a(n-6) for n > 6; a(1)=925, a(2)=967, a(3)=1013, a(4)=4537, a(5)=4835, a(6)=5153.
%F A159701 G.f.: (1-x)*(925+1892*x+2905*x^2+1892*x^3+925*x^4) / (1-6*x^3+x^6).
%F A159701 a(3*k-1) = 967*A001653(k) for k >= 1.
%e A159701 (-43, a(1)) = (-43, 925) is a solution: (-43)^2+(-43+967)^2 = 1849+853776 = 855625 = 925^2.
%e A159701 (A130017(1), a(2)) = (0, 967) is a solution: 0^2+(0+967)^2 = 935089 = 967^2.
%e A159701 (A130017(3), a(4)) = (2688, 4537) is a solution: 2688^2+(2688+967)^2 = 7225344+13359025 = 20584369 = 4537^2.
%t A159701 LinearRecurrence[{0,0,6,0,0,-1}, {925,967,1013,4537,4835,5153}, 40] (* _G. C. Greubel_, May 22 2018 *)
%o A159701 (PARI) {forstep(n=-44, 10000000, [1, 3], if(issquare(2*n^2+1934*n+935089, &k), print1(k, ",")))};
%o A159701 (PARI) x='x+O('x^30); Vec((1-x)*(925+1892*x+2905*x^2+1892*x^3+925*x^4)/( 1-6*x^3+x^6)) \\ _G. C. Greubel_, May 22 2018
%o A159701 (Magma) I:=[925,967,1013,4537,4835,5153]; [n le 6 select I[n] else 6*Self(n-3) - Self(n-6): n in [1..30]]; // _G. C. Greubel_, May 22 2018
%Y A159701 Cf. A130017, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A159702 (decimal expansion of (969+44*sqrt(2))/967), A159703 (decimal expansion of (2487411+1629850*sqrt(2))/967^2).
%K A159701 nonn,easy
%O A159701 1,1
%A A159701 _Klaus Brockhaus_, Apr 21 2009