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%I #37 Feb 06 2023 17:34:21
%S 1,24,70,139,231,346,484,645,829,1036,1266,1519,1795,2094,2416,2761,
%T 3129,3520,3934,4371,4831,5314,5820,6349,6901,7476,8074,8695,9339,
%U 10006
%N Centered 23-gonal numbers.
%H Ivan Panchenko, <a href="/A069174/b069174.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <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) = (23*n^2 - 23*n + 2)/2.
%F a(n) = 23*n+a(n-1)-23 (with a(1)=1). - _Vincenzo Librandi_, Aug 08 2010
%F From _Amiram Eldar_, Jun 21 2020: (Start)
%F Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(15/23)*Pi/2)/sqrt(345).
%F Sum_{n>=1} a(n)/n! = 25*e/2 - 1.
%F Sum_{n>=1} (-1)^n * a(n)/n! = 25/(2*e) - 1. (End)
%F E.g.f.: exp(x)*(1 + 23*x^2/2)-1. - _Nikolaos Pantelidis_, Feb 06 2023
%t FoldList[#1 + #2 &, 1, 23 Range@ 45] (* _Robert G. Wilson v_, Feb 02 2011 *)
%o (PARI) a(n)=(23*n^2-23*n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. centered polygonal numbers listed in A069190.
%K nonn,easy
%O 1,2
%A _Terrel Trotter, Jr._, Apr 09 2002
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