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 A069173 #44 Feb 16 2025 08:32:45
%S A069173 1,23,67,133,221,331,463,617,793,991,1211,1453,1717,2003,2311,2641,
%T A069173 2993,3367,3763,4181,4621,5083,5567,6073,6601,7151,7723,8317,8933,
%U A069173 9571,10231,10913,11617,12343,13091,13861,14653,15467,16303,17161,18041,18943,19867,20813
%N A069173 Centered 22-gonal numbers.
%H A069173 Ivan Panchenko, <a href="/A069173/b069173.txt">Table of n, a(n) for n = 1..1000</a>
%H A069173 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Numbers</a>.
%H A069173 R. Yin, J. Mu, and T. Komatsu, <a href="https://doi.org/10.20944/preprints202407.2280.v1">The p-Frobenius Number for the Triple of the Generalized Star Numbers</a>, Preprints 2024, 2024072280. See p. 2.
%H A069173 <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>.
%H A069173 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A069173 a(n) = 11*n^2 - 11*n + 1.
%F A069173 a(n) = 22*n + a(n-1) - 22 (with a(1)=1). - _Vincenzo Librandi_, Aug 08 2010
%F A069173 From _Amiram Eldar_, Jun 21 2020: (Start)
%F A069173 Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7/11)*Pi/2)/sqrt(77).
%F A069173 Sum_{n>=1} a(n)/n! = 12*e - 1.
%F A069173 Sum_{n>=1} (-1)^n * a(n)/n! = 12/e - 1. (End)
%F A069173 E.g.f.: exp(x)*(1 + 11 * x^2) - 1. - _Nikolaos Pantelidis_, Feb 06 2023
%F A069173 From _Elmo R. Oliveira_, Oct 22 2024: (Start)
%F A069173 G.f.: x*(1 + 20*x + x^2)/(1 - x)^3.
%F A069173 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%e A069173 a(5) = 221 because 11*5^2 - 11*5 + 1 = 275 - 55 + 1 = 221
%e A069173 For n=2, a(2)=22*2+1-22=23; n=3, a(3)=22*3+23-22=67; n=4, a(4)=22*4+67-22=133.
%t A069173 FoldList[#1 + #2 &, 1, 22 Range@ 45] (* _Robert G. Wilson v_, Feb 02 2011 *)
%o A069173 (PARI) a(n)=11*n^2-11*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A069173 Cf. centered polygonal numbers listed in A069190.
%K A069173 easy,nonn
%O A069173 1,2
%A A069173 _Terrel Trotter, Jr._, Apr 09 2002