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 A051872 #68 Feb 05 2023 14:43:09
%S A051872 0,1,20,57,112,185,276,385,512,657,820,1001,1200,1417,1652,1905,2176,
%T A051872 2465,2772,3097,3440,3801,4180,4577,4992,5425,5876,6345,6832,7337,
%U A051872 7860,8401,8960,9537,10132,10745,11376,12025,12692,13377,14080
%N A051872 20-gonal (or icosagonal) numbers: a(n) = n*(9*n-8).
%C A051872 This sequence does not contain any squares other than 0 and 1. See A188896. - _T. D. Noe_, Apr 13 2011
%C A051872 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
%C A051872 This is also a star decagonal number: a(n) = A001107(n) + 10*A000217(n-1). - _Luciano Ancora_, Mar 30 2015
%D A051872 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
%D A051872 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
%H A051872 Ivan Panchenko, <a href="/A051872/b051872.txt">Table of n, a(n) for n = 0..1000</a>
%H A051872 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A051872 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A051872 a(n) = 18*n + a(n-1) - 17, with n > 0, a(0) = 0. - _Vincenzo Librandi_, Aug 06 2010
%F A051872 G.f.: x*(1+17*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011
%F A051872 a(18*a(n) + 154*n + 1) = a(18*a(n) + 154*n) + a(18*n + 1). - _Vladimir Shevelev_, Jan 24 2014
%F A051872 Product_{n>=2} (1 - 1/a(n)) = 9/10. - _Amiram Eldar_, Jan 22 2021
%F A051872 For n>0, a(n) = A002378(3*n-2) + n - 2. - _Charlie Marion_, Jul 18 2022
%F A051872 E.g.f.: exp(x)*(x + 9*x^2). - _Nikolaos Pantelidis_, Feb 05 2023
%p A051872 A051872 := proc(n) n*(9*n-8) ;end proc: seq(A051872(n),n=0..30) ; # _R. J. Mathar_, Feb 05 2011
%t A051872 Table[9n^2 - 8n, {n, 0, 59}] (* _Alonso del Arte_, Dec 20 2014 *)
%t A051872 PolygonalNumber[20,Range[0,50]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 14 2017 *)
%o A051872 (PARI) n*(9*n-8) \\ _Charles R Greathouse IV_, Jan 24 2014
%K A051872 nonn,easy
%O A051872 0,3
%A A051872 _N. J. A. Sloane_, Dec 15 1999