%I
%S 1,23,67,133,221,331,463,617,793,991,1211,1453,1717,2003,2311,2641,
%T 2993,3367,3763,4181,4621,5083,5567,6073,6601,7151,7723,8317,8933,9571
%N Centered 22gonal numbers.
%H Ivan Panchenko, <a href="/A069173/b069173.txt">Table of n, a(n) for n = 1..1000</a>
%H E. Weisstein, <a href="http://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Numbers</a>
%H <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,1).
%F a(n) = 11n^2  11n + 1.
%F a(n) = 22*n+a(n1)22 (with a(1)=1).  _Vincenzo Librandi_, Aug 08 2010
%F From _Amiram Eldar_, Jun 21 2020: (Start)
%F Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7/11)*Pi/2)/sqrt(77).
%F Sum_{n>=1} a(n)/n! = 12*e  1.
%F Sum_{n>=1} (1)^n * a(n)/n! = 12/e  1. (End)
%e a(5) = 221 because 11*5^2  11*5 + 1 = 275  55 + 1 = 221
%e For n=2, a(2)=22*2+122=23; n=3, a(3)=22*3+2322=67; n=4, a(4)=22*4+6722=133.
%t FoldList[#1 + #2 &, 1, 22 Range@ 45] (* _Robert G. Wilson v_, Feb 02 2011 *)
%o (PARI) a(n)=11*n^211*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. centered polygonal numbers listed in A069190.
%K easy,nonn
%O 1,2
%A _Terrel Trotter, Jr._, Apr 09 2002
