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 A132354 #31 Mar 15 2022 04:33:39
%S A132354 0,5,9,24,32,57,69,104,120,165,185,240,264,329,357,432,464,549,585,
%T A132354 680,720,825,869,984,1032,1157,1209,1344,1400,1545,1605,1760,1824,
%U A132354 1989,2057,2232,2304,2489,2565,2760,2840,3045,3129,3344,3432,3657,3749,3984,4080
%N A132354 Integers m such that 7*m + 1 is a square.
%C A132354 Numbers of the form m*(7*m + 2) for m = 0, -1, 1, -2, 2, -3, 3, ... - _Bruno Berselli_, Feb 26 2018
%H A132354 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A132354 a(2*k) = k*(7*k + 2), a(2*k + 1) = 7*k^2 + 12*k + 5.
%F A132354 a(n) = n^2 + n + 3*ceiling(n/2)^2. - _Gary Detlefs_, Feb 23 2010
%F A132354 G.f.: -x*(5*x^2 + 4*x + 5)/((x - 1)^3*(x + 1)^2). - _Colin Barker_, Oct 24 2012
%F A132354 Sum_{n>=1} 1/a(n) = 7/4 - cot(2*Pi/7)*Pi/2. - _Amiram Eldar_, Mar 15 2022
%p A132354 seq(n^2+n+3*ceil(n/2)^2, n=0..48); # _Gary Detlefs_, Feb 23 2010
%t A132354 f[n_]:=IntegerQ[Sqrt[1+7*n]]; Select[Range[0,8! ],f[ # ]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2010 *)
%o A132354 (Magma) [n^2+n+3*Ceiling(n/2)^2: n in [0..50]]; // _Wesley Ivan Hurt_, Jul 07 2014
%Y A132354 Cf. A054000, A056220, A000217, A087475, A028347, A062717, A036666, A002378, A001082, A046092, A005563.
%K A132354 nonn,easy
%O A132354 0,2
%A A132354 _Mohamed Bouhamida_, Nov 08 2007
%E A132354 More terms from _Max Alekseyev_, Nov 13 2009
%E A132354 Better definition from _Max Alekseyev_, Oct 24 2012