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 A195314 #38 Nov 15 2024 09:06:03
%S A195314 1,29,85,169,281,421,589,785,1009,1261,1541,1849,2185,2549,2941,3361,
%T A195314 3809,4285,4789,5321,5881,6469,7085,7729,8401,9101,9829,10585,11369,
%U A195314 12181,13021,13889,14785,15709,16661,17641,18649,19685,20749,21841,22961,24109,25285,26489
%N A195314 Centered 28-gonal numbers.
%C A195314 Sequence found by reading the line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Semi-axis opposite to A144555 in the same spiral.
%H A195314 Vincenzo Librandi, <a href="/A195314/b195314.txt">Table of n, a(n) for n = 1..10000</a>
%H A195314 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195314 a(n) = 14*n^2 - 14*n + 1.
%F A195314 G.f.: -x*(1 + 26*x + x^2)/(x-1)^3. - _R. J. Mathar_, Sep 18 2011
%F A195314 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Oct 01 2011
%F A195314 Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(5/7)*Pi/2)/(2*sqrt(35)). - _Amiram Eldar_, Feb 11 2022
%F A195314 From _Elmo R. Oliveira_, Nov 14 2024: (Start)
%F A195314 E.g.f.: exp(x)*(14*x^2 + 1) - 1.
%F A195314 a(n) = 2*A069127(n) - 1. (End)
%t A195314 Table[14n^2-14n+1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,29,85},50]
%o A195314 (Magma) [(14*n^2-14*n+1): n in [1..50]]; // _Vincenzo Librandi_, Sep 19 2011
%o A195314 (PARI) a(n)=14*n^2-14*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195314 Bisection of A195145.
%Y A195314 Cf. A003154, A069129, A069133, A069190, A195315, A195316, A195317, A195318.
%Y A195314 Cf. A069127, A118277, A144555.
%K A195314 nonn,easy
%O A195314 1,2
%A A195314 _Omar E. Pol_, Sep 16 2011