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
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).
Crossrefs
Cf. centered polygonal numbers listed in A069190.
Programs
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Mathematica
FoldList[#1 + #2 &, 1, 23 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)
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PARI
a(n)=(23*n^2-23*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017
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