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 A255845 #39 Jan 25 2025 12:47:05
%S A255845 10,12,18,28,42,60,82,108,138,172,210,252,298,348,402,460,522,588,658,
%T A255845 732,810,892,978,1068,1162,1260,1362,1468,1578,1692,1810,1932,2058,
%U A255845 2188,2322,2460,2602,2748,2898,3052,3210,3372,3538,3708,3882,4060,4242,4428
%N A255845 a(n) = 2*n^2 + 10.
%C A255845 This is the case k=5 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.
%C A255845 Equivalently, numbers m such that 2*m - 20 is a square.
%H A255845 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A255845 a(n) = 2*A117951(n).
%F A255845 From _Vincenzo Librandi_, Mar 08 2015: (Start)
%F A255845 G.f.: 2*(5 - 9*x + 6*x^2)/(1 - x)^3.
%F A255845 a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A255845 From _Amiram Eldar_, Mar 28 2023: (Start)
%F A255845 Sum_{n>=0} 1/a(n) = (1 + sqrt(5)*Pi*coth(sqrt(5)*Pi))/20.
%F A255845 Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(5)*Pi*cosech(sqrt(5)*Pi))/20. (End)
%F A255845 E.g.f.: 2*exp(x)*(5 + x + x^2). - _Elmo R. Oliveira_, Jan 25 2025
%t A255845 Table[2 n^2 + 10, {n, 0, 50}]
%o A255845 (Magma) [2*n^2+10: n in [0..50]]; // _Vincenzo Librandi_, Mar 08 2015
%o A255845 (PARI) a(n)=2*n^2+10 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A255845 Cf. A016825 (first differences), A117951.
%Y A255845 Subsequence of A047463.
%Y A255845 Cf. similar sequences listed in A255843.
%K A255845 nonn,easy
%O A255845 0,1
%A A255845 _Avi Friedlich_, Mar 08 2015
%E A255845 Edited by _Bruno Berselli_, Mar 13 2015