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 A195318 #27 Nov 15 2024 13:10:53
%S A195318 1,45,133,265,441,661,925,1233,1585,1981,2421,2905,3433,4005,4621,
%T A195318 5281,5985,6733,7525,8361,9241,10165,11133,12145,13201,14301,15445,
%U A195318 16633,17865,19141,20461,21825,23233,24685,26181,27721,29305,30933,32605,34321,36081,37885,39733
%N A195318 Centered 44-gonal numbers.
%C A195318 Sequence found by reading the line from 1, in the direction 1, 45, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Semi-axis opposite to A195323 in the same spiral.
%H A195318 Vincenzo Librandi, <a href="/A195318/b195318.txt">Table of n, a(n) for n = 1..10000</a>
%H A195318 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195318 a(n) = 22*n^2 - 22*n + 1.
%F A195318 Sum_{n>=1} 1/a(n) = Pi*tan(3*Pi/(2*sqrt(11)))/(6*sqrt(11)). - _Amiram Eldar_, Feb 11 2022
%F A195318 G.f.: -x*(1+42*x+x^2)/(x-1)^3. - _R. J. Mathar_, May 07 2024
%F A195318 From _Elmo R. Oliveira_, Nov 15 2024: (Start)
%F A195318 E.g.f.: exp(x)*(22*x^2 + 1) - 1.
%F A195318 a(n) = 2*A069173(n) - 1.
%F A195318 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A195318 Table[22n^2-22n+1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,45,133},50] (* _Harvey P. Dale_, Mar 16 2019 *)
%o A195318 (Magma) [22*n^2 - 22*n + 1: n in [1..50]]; // _Vincenzo Librandi_, Sep 21 2011
%o A195318 (PARI) a(n)=22*n^2-22*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195318 Bisection of A195149.
%Y A195318 Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195316, A195317.
%Y A195318 Cf. A069173, A195313, A195323.
%K A195318 nonn,easy
%O A195318 1,2
%A A195318 _Omar E. Pol_, Sep 16 2011