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A069174 Centered 23-gonal numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

E. Weisstein, 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)

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 A320702

Adjacent sequences:  A069171 A069172 A069173 * A069175 A069176 A069177

KEYWORD

nonn,easy

AUTHOR

Terrel Trotter, Jr., Apr 09 2002

STATUS

approved

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Last modified August 7 15:30 EDT 2020. Contains 336276 sequences. (Running on oeis4.)