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 A276602 #30 Sep 08 2022 08:46:17
%S A276602 0,9,54,315,1836,10701,62370,363519,2118744,12348945,71974926,
%T A276602 419500611,2445028740,14250671829,83059002234,484103341575,
%U A276602 2821561047216,16445262941721,95850016603110,558654836676939,3256079003458524,18977819184074205,110610836100986706
%N A276602 Values of k such that k^2 + 10 is a triangular number (A000217).
%H A276602 Colin Barker, <a href="/A276602/b276602.txt">Table of n, a(n) for n = 1..1000</a>
%H A276602 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H A276602 Soumeya M. Tebtoub, Hacène Belbachir and László Németh, <a href="https://hal.archives-ouvertes.fr/hal-02918958/document#page=18">Integer sequences and ellipse chains inside a hyperbola</a>, Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), hal-02918958 [math.cs], 17-18.
%H A276602 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A276602 a(n) = (9/(4*sqrt(2))*( (3 - 2*sqrt(2))*(3 + 2*sqrt(2))^n - (3 + 2*sqrt(2))*(3 - 2*sqrt(2))^n) ).
%F A276602 a(n) = 9*A001109(n-1).
%F A276602 a(n) = 6*a(n-1) - a(n-2) for n>2.
%F A276602 G.f.: 9*x^2 / (1-6*x+x^2).
%F A276602 a(n) = (9/2)*A000129(2*n-2). - _G. C. Greubel_, Sep 15 2021
%e A276602 9 is in the sequence because 9^2+10 = 91, which is a triangular number.
%t A276602 CoefficientList[Series[9*x/(1 - 6*x + x^2), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Sep 07 2016 *)
%t A276602 (9/2)*Fibonacci[2*(Range[30] -1), 2] (* _G. C. Greubel_, Sep 15 2021 *)
%o A276602 (PARI) concat(0, Vec(9*x^2/(1-6*x+x^2) + O(x^30)))
%o A276602 (Magma) [n le 2 select 9*(n-1) else 6*Self(n-1) - Self(n-2): n in [1..31]]; // _G. C. Greubel_, Sep 15 2021
%o A276602 (Sage) [(9/2)*lucas_number1(2*n-2, 2, -1) for n in (1..30)] # _G. C. Greubel_, Sep 15 2021
%Y A276602 Cf. A000129, A000217, A230044.
%Y A276602 Cf. A001109 (k=0), A106328 (k=1), A077241 (k=2), A276598 (k=3), A276599 (k=5), A276600 (k=6), A276601 (k=9), where k is the value added to n^2.
%K A276602 nonn,easy
%O A276602 1,2
%A A276602 _Colin Barker_, Sep 07 2016