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 A195143 #62 Jan 16 2023 08:53:11
%S A195143 0,1,12,25,48,73,108,145,192,241,300,361,432,505,588,673,768,865,972,
%T A195143 1081,1200,1321,1452,1585,1728,1873,2028,2185,2352,2521,2700,2881,
%U A195143 3072,3265,3468,3673,3888,4105,4332,4561,4800,5041,5292,5545,5808,6073,6348
%N A195143 a(n) = n-th concentric 12-gonal number.
%C A195143 Concentric dodecagonal numbers. [corrected by _Ivan Panchenko_, Nov 09 2013]
%C A195143 Sequence found by reading the line from 0, in the direction 0, 12,..., and the same line from 1, in the direction 1, 25,..., in the square spiral whose vertices are the generalized octagonal numbers A001082. Main axis, perpendicular to A028896 in the same spiral.
%C A195143 Partial sums of A091998. - _Reinhard Zumkeller_, Jan 07 2012
%C A195143 Column 12 of A195040. - _Omar E. Pol_, Sep 28 2011
%H A195143 Vincenzo Librandi, <a href="/A195143/b195143.txt">Table of n, a(n) for n = 0..10000</a>
%H A195143 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A195143 From _Vincenzo Librandi_, Sep 27 2011: (Start)
%F A195143 a(n) = 3*n^2+(-1)^n-1.
%F A195143 a(n) = -a(n-1) + 6*n^2 - 6*n + 1. (End)
%F A195143 G.f.: -x*(1+10*x+x^2) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Sep 18 2011
%F A195143 a(n) = Sum_{k=1..n} (2*(-1)^(n-k+1) + 3*(2*k-1)), n>0, a(0) = 0. - _L. Edson Jeffery_, Sep 14 2014
%F A195143 Sum_{n>=1} 1/a(n) = Pi^2/72 + tan(Pi/sqrt(6))*Pi/(4*sqrt(6)). - _Amiram Eldar_, Jan 16 2023
%t A195143 Table[Sum[2*(-1)^(n - k + 1) + 6*k - 3, {k, n}], {n, 0, 47}] (* _L. Edson Jeffery_, Sep 14 2014 *)
%o A195143 (Magma) [(3*n^2+(-1)^n-1): n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o A195143 (Haskell)
%o A195143 a195143 n = a195143_list !! n
%o A195143 a195143_list = scanl (+) 0 a091998_list
%o A195143 -- _Reinhard Zumkeller_, Jan 07 2012
%Y A195143 A135453 and A069190 interleaved.
%Y A195143 Cf. A001082, A032527, A032528, A077221, A195043, A195045, A195040, A195142, A195145, A195146, A195147, A195148, A195149.
%Y A195143 Cf. A016921 (6n+1), A016969 (6n+5), A091998 (positive integers of the form 12*k +- 1), A092242 (positive integers of the form 12*k +- 5).
%K A195143 nonn,easy
%O A195143 0,3
%A A195143 _Omar E. Pol_, Sep 17 2011