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 A152746 #40 Mar 30 2023 02:37:14
%S A152746 0,6,36,90,168,270,396,546,720,918,1140,1386,1656,1950,2268,2610,2976,
%T A152746 3366,3780,4218,4680,5166,5676,6210,6768,7350,7956,8586,9240,9918,
%U A152746 10620,11346,12096,12870,13668,14490,15336,16206,17100
%N A152746 Six times hexagonal numbers: 6*n*(2*n-1).
%C A152746 Sequence found by reading the line from 0, in the direction 0, 6, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - _Omar E. Pol_, Sep 18 2011
%C A152746 a(n) is the number of walks on a cubic lattice of n dimensions that return to the origin, not necessarily for the first time, after 4 steps. - _Shel Kaphan_, Mar 20 2023
%H A152746 Ivan Panchenko, <a href="/A152746/b152746.txt">Table of n, a(n) for n = 0..1000</a>
%H A152746 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152746 a(n) = 12*n^2 - 6*n = A000384(n)*6 = A002939(n)*3 = A094159(n)*2.
%F A152746 a(n) = a(n-1) + 24*n - 18 (with a(0)=0). - _Vincenzo Librandi_, Nov 26 2010
%F A152746 From _G. C. Greubel_, Sep 01 2018: (Start)
%F A152746 G.f.: 6*x*(1+3*x)/(1-x)^3.
%F A152746 E.g.f.: 6*x*(1+2*x)*exp(x). (End)
%F A152746 From _Amiram Eldar_, Mar 30 2023: (Start)
%F A152746 Sum_{n>=1} 1/a(n) = log(2)/3.
%F A152746 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/12 - log(2)/6. (End)
%t A152746 6*PolygonalNumber[6,Range[0,40]] (* The program uses the PolygonalNumber function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 04 2016 *)
%t A152746 LinearRecurrence[{3,-3,1}, {0,6,36}, 50] (* or *) Table[6*n*(2*n-1), {n,0,50}] (* _G. C. Greubel_, Sep 01 2018 *)
%o A152746 (PARI) a(n)=6*n*(2*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A152746 (Magma) [6*n*(2*n-1): n in [0..50]]; // _G. C. Greubel_, Sep 01 2018
%Y A152746 Cf. A000384, A001082, A002939, A094159, A085250, A152745.
%Y A152746 Column n=2 of A287318.
%K A152746 easy,nonn,walk
%O A152746 0,2
%A A152746 _Omar E. Pol_, Dec 12 2008