A069173 Centered 22-gonal numbers.

1, 23, 67, 133, 221, 331, 463, 617, 793, 991, 1211, 1453, 1717, 2003, 2311, 2641, 2993, 3367, 3763, 4181, 4621, 5083, 5567, 6073, 6601, 7151, 7723, 8317, 8933, 9571

Offset

1,2

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Centered Polygonal Numbers

Index entries for sequences related to centered polygonal numbers

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 11*n^2 - 11*n + 1.

a(n) = 22*n+a(n-1)-22 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010

From Amiram Eldar, Jun 21 2020: (Start)

Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7/11)*Pi/2)/sqrt(77).

Sum_{n>=1} a(n)/n! = 12*e - 1.

Sum_{n>=1} (-1)^n * a(n)/n! = 12/e - 1. (End)

E.g.f.: exp(x)*(1 + 11 * x^2) -1. - Nikolaos Pantelidis, Feb 06 2023

Example

a(5) = 221 because 11*5^2 - 11*5 + 1 = 275 - 55 + 1 = 221
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.

Mathematica

FoldList[#1 + #2 &, 1, 22 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)

Prog

(PARI) a(n)=11*n^2-11*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. centered polygonal numbers listed in A069190.

Sequence in context: A053559 A322414 A031376 * A124716 A139955 A126377

Adjacent sequences: A069170 A069171 A069172 * A069174 A069175 A069176

Keyword

easy,nonn

Author

Terrel Trotter, Jr., Apr 09 2002

Status

approved