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 A051872 20-gonal (or icosagonal) numbers: a(n) = n*(9*n-8). 12
 0, 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, 1417, 1652, 1905, 2176, 2465, 2772, 3097, 3440, 3801, 4180, 4577, 4992, 5425, 5876, 6345, 6832, 7337, 7860, 8401, 8960, 9537, 10132, 10745, 11376, 12025, 12692, 13377, 14080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence does not contain any squares other than 0 and 1. See A188896. - T. D. Noe, Apr 13 2011 Sequence found by reading the line from 0, in the direction 0, 20,... and the parallel line from 1, in the direction 1, 57,..., in the square spiral whose vertices are the generalized 20-gonal numbers. - Omar E. Pol, Jul 18 2012 This is also a star decagonal number: a(n) = A001107(n) + 10*A000217(n-1). - Luciano Ancora, Mar 30 2015 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189. E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 18*n + a(n-1) - 17, with n > 0, a(0) = 0. - Vincenzo Librandi, Aug 06 2010 G.f.: x*(1+17*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 a(18*a(n) + 154*n + 1) = a(18*a(n) + 154*n) + a(18*n + 1). - Vladimir Shevelev, Jan 24 2014 MAPLE A051872 := proc(n) n*(9*n-8) ; end proc: seq(A051872(n), n=0..30) ; # R. J. Mathar, Feb 05 2011 MATHEMATICA Table[9n^2 - 8n, {n, 0, 59}] (* Alonso del Arte, Dec 20 2014 *) PolygonalNumber[20, Range[0, 50]] (* Requires Mathematica version 10 or later *)  (* Harvey P. Dale, May 14 2017 *) PROG (PARI) n*(9*n-8) \\ Charles R Greathouse IV, Jan 24 2014 CROSSREFS Sequence in context: A109806 A216267 A012483 * A297397 A104100 A069132 Adjacent sequences:  A051869 A051870 A051871 * A051873 A051874 A051875 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)