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 A051871 19-gonal (or enneadecagonal) numbers: n(17n-15)/2. 9
 0, 1, 19, 54, 106, 175, 261, 364, 484, 621, 775, 946, 1134, 1339, 1561, 1800, 2056, 2329, 2619, 2926, 3250, 3591, 3949, 4324, 4716, 5125, 5551, 5994, 6454, 6931, 7425, 7936, 8464, 9009, 9571, 10150, 10746, 11359, 11989, 12636, 13300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence found by reading the line from 0, in the direction 0, 19, ... and the parallel line from 1, in the direction 1, 54, ..., in the square spiral whose vertices are the generalized 19-gonal numbers. - Omar E. Pol, Jul 18 2012. Partial sums of A215137 = 17n + 1. - Jeremy Gardiner, Aug 04 2012 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189. Elena Deza and Michel M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6. LINKS Jeremy Gardiner, Table of n, a(n) for n = 0..999 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = n(17n-15)/2. G.f.: x*(1+16*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 a(n) = 17*n + a(n-1) - 16 (with a(0) = 0). - Vincenzo Librandi, Aug 06 2010 a(17*a(n) + 137*n + 1) = a(17*a(n) + 137*n) + a(17*n+1). - Vladimir Shevelev, Jan 24 2014 EXAMPLE a(1) = 17 * 1 + 0 - 16 = 1. a(2) = 17 * 2 + 1 - 16 = 19. a(3) = 17 * 3 + 19 - 16 = 54. - Vincenzo Librandi, Aug 06 2010 MAPLE A051871 := proc(n) n*(17*n-15)/2 ; end proc: seq(A051871(n), n=0..30) ; # R. J. Mathar, Feb 05 2011 MATHEMATICA Table[(17n^2 - 15n)/2, {n, 0, 39}] (* Alonso del Arte, Feb 19 2015 *) PROG (PARI) a(n)=n*(17*n-15)/2; \\ Charles R Greathouse IV, Jan 24 2014 CROSSREFS Sequence in context: A142072 A221594 A288144 * A044121 A044502 A069131 Adjacent sequences:  A051868 A051869 A051870 * A051872 A051873 A051874 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)