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 A255847 #28 Jan 25 2025 15:03:10
%S A255847 16,18,24,34,48,66,88,114,144,178,216,258,304,354,408,466,528,594,664,
%T A255847 738,816,898,984,1074,1168,1266,1368,1474,1584,1698,1816,1938,2064,
%U A255847 2194,2328,2466,2608,2754,2904,3058,3216,3378,3544,3714,3888,4066,4248,4434,4624
%N A255847 a(n) = 2*n^2 + 16.
%C A255847 This is the case k=8 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.
%C A255847 Equivalently, numbers m such that 2*m - 32 is a square.
%H A255847 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A255847 G.f.: 2*(8 - 15*x + 9*x^2)/(1 - x)^3.
%F A255847 a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A255847 a(n) = 2*A189833(n).
%F A255847 From _Amiram Eldar_, Mar 28 2023: (Start)
%F A255847 Sum_{n>=0} 1/a(n) = (1 + 2*sqrt(2)*Pi*coth(2*sqrt(2)*Pi))/32.
%F A255847 Sum_{n>=0} (-1)^n/a(n) = (1 + 2*sqrt(2)*Pi*cosech(2*sqrt(2)*Pi))/32. (End)
%F A255847 E.g.f.: 2*exp(x)*(8 + x + x^2). - _Elmo R. Oliveira_, Jan 25 2025
%t A255847 Table[2 n^2 + 16, {n, 0, 50}]
%t A255847 LinearRecurrence[{3,-3,1},{16,18,24},50] (* _Harvey P. Dale_, Nov 11 2017 *)
%o A255847 (PARI) vector(50, n, n--; 2*n^2+16)
%o A255847 (Sage) [2*n^2+16 for n in (0..50)]
%o A255847 (Magma) [2*n^2+16: n in [0..50]];
%Y A255847 Cf. A189833.
%Y A255847 Subsequence of A047467.
%Y A255847 Cf. similar sequences listed in A255843.
%K A255847 nonn,easy
%O A255847 0,1
%A A255847 _Avi Friedlich_, Mar 08 2015
%E A255847 Edited by _Bruno Berselli_, Mar 13 2015