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 A051873 21-gonal numbers: a(n) = n*(19n - 17)/2. 8
 0, 1, 21, 60, 118, 195, 291, 406, 540, 693, 865, 1056, 1266, 1495, 1743, 2010, 2296, 2601, 2925, 3268, 3630, 4011, 4411, 4830, 5268, 5725, 6201, 6696, 7210, 7743, 8295, 8866, 9456, 10065, 10693, 11340, 12006, 12691, 13395, 14118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence found by reading the line from 0, in the direction 0, 21, ... and the parallel line from 1, in the direction 1, 60, ..., in the square spiral whose vertices are the generalized 21-gonal numbers. - Omar E. Pol, Jul 18 2012 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 Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: x*(1+18*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 a(n) = 19*n+a(n-1)-18 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010 a(n) = A226490(n) - n. - Bruno Berselli, Jun 11 2013 a(19*a(n)+172*n+1) = a(19*a(n)+172*n) + a(19*n+1). - Vladimir Shevelev, Jan 24 2014 MAPLE A051873 := proc(n) n*(19*n-17)/2 ; end proc: seq(A051873(n), n=0..30) ; # R. J. Mathar, Feb 05 2011 MATHEMATICA s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 19}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *) PolygonalNumber[21, Range[0, 40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 22 2016 *) Table[n*(19*n - 17)/2, {n, 0, 100}] (* Robert Price, Oct 11 2018 *) PROG (PARI) n*(19*n-17)/2 \\ Charles R Greathouse IV, Jan 24 2014 CROSSREFS Sequence in context: A020148 A037305 A223467 * A223460 A219690 A325319 Adjacent sequences:  A051870 A051871 A051872 * A051874 A051875 A051876 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)