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 A195317 #34 Nov 15 2024 13:10:49
%S A195317 1,41,121,241,401,601,841,1121,1441,1801,2201,2641,3121,3641,4201,
%T A195317 4801,5441,6121,6841,7601,8401,9241,10121,11041,12001,13001,14041,
%U A195317 15121,16241,17401,18601,19841,21121,22441,23801,25201,26641,28121,29641,31201,32801,34441,36121
%N A195317 Centered 40-gonal numbers.
%C A195317 Also centered tetracontagonal numbers or centered tetrakaicontagonal numbers. Also sequence found by reading the line from 1, in the direction 1, 41, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semi-axis opposite to A195322 in the same spiral.
%H A195317 Vincenzo Librandi, <a href="/A195317/b195317.txt">Table of n, a(n) for n = 1..10000</a>
%H A195317 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195317 a(n) = 20*n^2 - 20*n + 1.
%F A195317 Sum_{n>=1} 1/a(n) = Pi*tan(Pi/sqrt(5))/(8*sqrt(5)). - _Amiram Eldar_, Feb 11 2022
%F A195317 G.f.: -x*(1+38*x+x^2)/(x-1)^3. - _R. J. Mathar_, May 07 2024
%F A195317 From _Elmo R. Oliveira_, Nov 15 2024: (Start)
%F A195317 E.g.f.: exp(x)*(20*x^2 + 1) - 1.
%F A195317 a(n) = 2*A069133(n) - 1.
%F A195317 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A195317 Table[20*n^2 - 20*n + 1, {n, 1, 40}] (* _Amiram Eldar_, Feb 11 2022 *)
%o A195317 (Magma) [20*n^2 - 20*n + 1: n in [1..50]]; // _Vincenzo Librandi_, Sep 21 2011
%o A195317 (PARI) a(n)=20*n^2-20*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195317 Bisection of A195148.
%Y A195317 Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195316, A195318.
%Y A195317 Cf. A195162, A195322.
%K A195317 nonn,easy
%O A195317 1,2
%A A195317 _Omar E. Pol_, Sep 16 2011