This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051871 #53 Feb 06 2023 07:06:07
%S A051871 0,1,19,54,106,175,261,364,484,621,775,946,1134,1339,1561,1800,2056,
%T A051871 2329,2619,2926,3250,3591,3949,4324,4716,5125,5551,5994,6454,6931,
%U A051871 7425,7936,8464,9009,9571,10150,10746,11359,11989,12636,13300
%N A051871 19-gonal (or enneadecagonal) numbers: n(17n-15)/2.
%C A051871 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
%C A051871 Partial sums of A215137 (17n + 1). - _Jeremy Gardiner_, Aug 04 2012
%D A051871 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
%D A051871 Elena Deza and Michel M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
%H A051871 Jeremy Gardiner, <a href="/A051871/b051871.txt">Table of n, a(n) for n = 0..999</a>
%H A051871 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A051871 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A051871 a(n) = n(17n-15)/2.
%F A051871 G.f.: x*(1+16*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011
%F A051871 a(n) = 17*n + a(n-1) - 16 (with a(0) = 0). - _Vincenzo Librandi_, Aug 06 2010
%F A051871 a(17*a(n) + 137*n + 1) = a(17*a(n) + 137*n) + a(17*n+1). - _Vladimir Shevelev_, Jan 24 2014
%F A051871 Product_{n>=2} (1 - 1/a(n)) = 17/19. - _Amiram Eldar_, Jan 22 2021
%F A051871 E.g.f.: exp(x)*(x + 17*x^2/2). - _Nikolaos Pantelidis_, Feb 06 2023
%e A051871 a(1) = 17 * 1 + 0 - 16 = 1.
%e A051871 a(2) = 17 * 2 + 1 - 16 = 19.
%e A051871 a(3) = 17 * 3 + 19 - 16 = 54. - _Vincenzo Librandi_, Aug 06 2010
%p A051871 A051871 := proc(n) n*(17*n-15)/2 ; end proc: seq(A051871(n),n=0..30) ; # _R. J. Mathar_, Feb 05 2011
%t A051871 Table[(17n^2 - 15n)/2, {n, 0, 39}] (* _Alonso del Arte_, Feb 19 2015 *)
%o A051871 (PARI) a(n)=n*(17*n-15)/2; \\ _Charles R Greathouse IV_, Jan 24 2014
%K A051871 nonn,easy
%O A051871 0,3
%A A051871 _N. J. A. Sloane_, Dec 15 1999