login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069173 Centered 22-gonal numbers. 6

%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 22-gonal 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(n-1)-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+1-22=23; n=3, a(3)=22*3+23-22=67; n=4, a(4)=22*4+67-22=133.

%t FoldList[#1 + #2 &, 1, 22 Range@ 45] (* _Robert G. Wilson v_, Feb 02 2011 *)

%o (PARI) a(n)=11*n^2-11*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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 03:20 EST 2020. Contains 338632 sequences. (Running on oeis4.)