A069174 Centered 23-gonal numbers.

1, 24, 70, 139, 231, 346, 484, 645, 829, 1036, 1266, 1519, 1795, 2094, 2416, 2761, 3129, 3520, 3934, 4371, 4831, 5314, 5820, 6349, 6901, 7476, 8074, 8695, 9339, 10006

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) = (23*n^2 - 23*n + 2)/2.

a(n) = 23*n+a(n-1)-23 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010

From Amiram Eldar, Jun 21 2020: (Start)

Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(15/23)*Pi/2)/sqrt(345).

Sum_{n>=1} a(n)/n! = 25*e/2 - 1.

Sum_{n>=1} (-1)^n * a(n)/n! = 25/(2*e) - 1. (End)

E.g.f.: exp(x)*(1 + 23*x^2/2)-1. - Nikolaos Pantelidis, Feb 06 2023

Mathematica

FoldList[#1 + #2 &, 1, 23 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)

Prog

(PARI) a(n)=(23*n^2-23*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. centered polygonal numbers listed in A069190.

Sequence in context: A319972 A304157 A051876 * A124717 A126378 A342800

Adjacent sequences: A069171 A069172 A069173 * A069175 A069176 A069177

Keyword

nonn,easy

Author

Terrel Trotter, Jr., Apr 09 2002

Status

approved