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 A069173 Centered 22-gonal numbers. 6
 1, 23, 67, 133, 221, 331, 463, 617, 793, 991, 1211, 1453, 1717, 2003, 2311, 2641, 2993, 3367, 3763, 4181, 4621, 5083, 5567, 6073, 6601, 7151, 7723, 8317, 8933, 9571 (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) = 11n^2 - 11n + 1. a(n) = 22*n+a(n-1)-22 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010 From Amiram Eldar, Jun 21 2020: (Start) Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7/11)*Pi/2)/sqrt(77). Sum_{n>=1} a(n)/n! = 12*e - 1. Sum_{n>=1} (-1)^n * a(n)/n! = 12/e - 1. (End) EXAMPLE a(5) = 221 because 11*5^2 - 11*5 + 1 = 275 - 55 + 1 = 221 For n=2, a(2)=22*2+1-22=23; n=3, a(3)=22*3+23-22=67; n=4, a(4)=22*4+67-22=133. MATHEMATICA FoldList[#1 + #2 &, 1, 22 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *) PROG (PARI) a(n)=11*n^2-11*n+1 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. centered polygonal numbers listed in A069190. Sequence in context: A053559 A322414 A031376 * A124716 A139955 A126377 Adjacent sequences:  A069170 A069171 A069172 * A069174 A069175 A069176 KEYWORD easy,nonn AUTHOR Terrel Trotter, Jr., Apr 09 2002 STATUS approved

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Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)