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 A152994 #35 Aug 06 2024 22:32:34
%S A152994 0,9,54,135,252,405,594,819,1080,1377,1710,2079,2484,2925,3402,3915,
%T A152994 4464,5049,5670,6327,7020,7749,8514,9315,10152,11025,11934,12879,
%U A152994 13860,14877,15930,17019,18144,19305,20502,21735,23004,24309,25650,27027,28440,29889,31374
%N A152994 Nine times hexagonal numbers: a(n) = 9*n*(2*n-1).
%C A152994 Sequence found by reading the line from 0, in the direction 0, 9,..., in the square spiral whose vertices are the generalized 11-gonal numbers A195160. - _Omar E. Pol_, Sep 18 2011
%H A152994 Ivan Panchenko, <a href="/A152994/b152994.txt">Table of n, a(n) for n = 0..1000</a>
%H A152994 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152994 a(n) = 18*n^2 - 9*n = A000384(n)*9 = A094159(n)*3.
%F A152994 a(n) = a(n-1) + 36*n - 27 for n>0, a(0)=0. - _Vincenzo Librandi_, Dec 15 2010
%F A152994 a(n) = Sum_{i = 2..10} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - _Bruno Berselli_, Jul 04 2018
%F A152994 From _G. C. Greubel_, Sep 01 2019: (Start)
%F A152994 G.f.: 9*x*(1+3*x)/(1-x)^3.
%F A152994 E.g.f.: 9*x*(1+2*x)*exp(x). (End)
%F A152994 From _Amiram Eldar_, Feb 27 2022: (Start)
%F A152994 Sum_{n>=1} 1/a(n) = 2*log(2)/9.
%F A152994 Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi - 2*log(2))/18. (End)
%p A152994 seq(9*n*(2*n-1), n=0..40); # _G. C. Greubel_, Sep 01 2019
%t A152994 Table[9*n*(2*n-1), {n,0,40}] (* _G. C. Greubel_, Sep 01 2019 *)
%t A152994 9*PolygonalNumber[6,Range[0,50]] (* _Harvey P. Dale_, Jul 24 2022 *)
%o A152994 (PARI) a(n)=9*n*(2*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A152994 (Magma) [9*n*(2*n-1): n in [0..40]]; // _G. C. Greubel_, Sep 01 2019
%o A152994 (Sage) [9*n*(2*n-1) for n in (0..40)] # _G. C. Greubel_, Sep 01 2019
%o A152994 (GAP) List([0..40], n-> 9*n*(2*n-1)); # _G. C. Greubel_, Sep 01 2019
%Y A152994 Cf. A000384, A094159.
%Y A152994 Similar sequences are listed in A316466.
%K A152994 nonn,easy
%O A152994 0,2
%A A152994 _Omar E. Pol_, Dec 22 2008