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 A051875 #53 Feb 06 2023 06:15:54
%S A051875 0,1,23,66,130,215,321,448,596,765,955,1166,1398,1651,1925,2220,2536,
%T A051875 2873,3231,3610,4010,4431,4873,5336,5820,6325,6851,7398,7966,8555,
%U A051875 9165,9796,10448,11121,11815,12530,13266,14023,14801,15600
%N A051875 23-gonal numbers: a(n) = n(21n-19)/2.
%C A051875 Sequence found by reading the line from 0, in the direction 0, 23, ..., and the parallel line from 1, in the direction 1, 66, ..., in the square spiral whose vertices are the generalized 23-gonal numbers. - _Omar E. Pol_, Jul 18 2012
%D A051875 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
%D A051875 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
%H A051875 Vincenzo Librandi, <a href="/A051875/b051875.txt">Table of n, a(n) for n = 0..1000</a>
%H A051875 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A051875 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A051875 G.f.: x*(1+20*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011
%F A051875 a(n) = 21*n + a(n-1) - 20 with n > 0, a(0) = 0. - _Vincenzo Librandi_, Aug 06 2010
%F A051875 a(n) = A226491(n) - n. - _Bruno Berselli_, Jun 11 2013
%F A051875 a(21*a(n)+211*n+1) = a(21*a(n)+211*n) + a(21*n+1). - _Vladimir Shevelev_, Jan 24 2014
%F A051875 Product_{n>=2} (1 - 1/a(n)) = 21/23. - _Amiram Eldar_, Jan 22 2021
%F A051875 E.g.f.: exp(x)*(x + 21*x^2/2). - _Nikolaos Pantelidis_, Feb 06 2023
%t A051875 CoefficientList[Series[x (1 + 20 x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 19 2013 *)
%t A051875 Table[(21n^2 - 19n)/2, {n, 0, 39}] (* _Alonso del Arte_, Jan 23 2015 *)
%t A051875 PolygonalNumber[23,Range[0,40]] (* _Harvey P. Dale_, Aug 01 2022 *)
%o A051875 (PARI) a(n)=n*(21*n-19)/2 \\ _Charles R Greathouse IV_, Jan 24 2014
%K A051875 nonn,easy
%O A051875 0,3
%A A051875 _N. J. A. Sloane_, Dec 15 1999