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