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 A069131 Centered 18-gonal numbers. 9
 1, 19, 55, 109, 181, 271, 379, 505, 649, 811, 991, 1189, 1405, 1639, 1891, 2161, 2449, 2755, 3079, 3421, 3781, 4159, 4555, 4969, 5401, 5851, 6319, 6805, 7309, 7831, 8371, 8929, 9505, 10099, 10711, 11341, 11989, 12655, 13339, 14041, 14761, 15499, 16255 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equals binomial transform of [1, 18, 18, 0, 0, 0,...]. Example: a(3) = 55 = (1, 2, 1) dot (1, 18, 18) = (1 + 36 + 18). - Gary W. Adamson, Aug 24 2010 Narayana transform (A001263) of [1, 18, 0, 0, 0,...]. - Gary W. Adamson, Jul 28 2011 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) = 9*n^2 - 9*n + 1. a(n) = 18*n+a(n-1)-18 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010 G.f.: ( x*(1+16*x+x^2) ) / ( (1-x)^3 ). - R. J. Mathar, Feb 04 2011 a(1)=1, a(2)=19, a(3)=55, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jan 20 2014 From Amiram Eldar, Jun 21 2020: (Start) Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(5)*Pi/6)/(3*sqrt(5)). Sum_{n>=1} a(n)/n! = 10*e - 1. Sum_{n>=1} (-1)^n * a(n)/n! = 10/e - 1. (End) EXAMPLE a(5)= 181 because 9*5^2 - 9*5 + 1 = 225 - 45 + 1 = 181. MATHEMATICA FoldList[#1 + #2 &, 1, 18 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *) LinearRecurrence[{3, -3, 1}, {1, 19, 55}, 50] (* Harvey P. Dale, Jan 20 2014 *) PROG (PARI) a(n)=9*n^2-9*n+1 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. centered polygonal numbers listed in A069190. Sequence in context: A051871 A044121 A044502 * A124712 A126373 A125818 Adjacent sequences:  A069128 A069129 A069130 * A069132 A069133 A069134 KEYWORD easy,nice,nonn AUTHOR Terrel Trotter, Jr., Apr 07 2002 STATUS approved

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Last modified October 22 05:01 EDT 2020. Contains 337950 sequences. (Running on oeis4.)