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 A069178 Centered 21-gonal numbers. 5
 1, 22, 64, 127, 211, 316, 442, 589, 757, 946, 1156, 1387, 1639, 1912, 2206, 2521, 2857, 3214, 3592, 3991, 4411, 4852, 5314, 5797, 6301, 6826, 7372, 7939, 8527, 9136, 9766, 10417, 11089, 11782, 12496, 13231, 13987, 14764, 15562, 16381, 17221, 18082, 18964 (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 linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = (21n^2 - 21n + 2)/2 a(n) = 21*n + a(n-1) - 21 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010 G.f. -x*(1+19*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011 Binomial transform of [1, 21, 21, 0, 0, 0,...] and Narayana transform (A001263) of [1, 21, 0, 0, 0,...]. - Gary W. Adamson, Jul 26 2011 a(n) = 1 + sum_{i=1..n} 21*(i-1). - Wesley Ivan Hurt, May 25 2013 From Amiram Eldar, Jun 21 2020: (Start) Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(13/21)*Pi/2)/sqrt(273). Sum_{n>=1} a(n)/n! = 23*e/2 - 1. Sum_{n>=1} (-1)^n * a(n)/n! = 23/(2*e) - 1. (End) MATHEMATICA FoldList[#1 + #2 &, 1, 21 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *) PROG (PARI) a(n)=(21*n^2-21*n+2)/2 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. centered polygonal numbers listed in A069190. Sequence in context: A221595 A051874 A140390 * A081929 A305064 A124715 Adjacent sequences:  A069175 A069176 A069177 * A069179 A069180 A069181 KEYWORD easy,nonn AUTHOR Terrel Trotter, Jr., Apr 09 2002 STATUS approved

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Last modified October 26 09:33 EDT 2020. Contains 338027 sequences. (Running on oeis4.)