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%I A051873 #60 Mar 19 2023 15:32:42
%S A051873 0,1,21,60,118,195,291,406,540,693,865,1056,1266,1495,1743,2010,2296,
%T A051873 2601,2925,3268,3630,4011,4411,4830,5268,5725,6201,6696,7210,7743,
%U A051873 8295,8866,9456,10065,10693,11340,12006,12691,13395,14118
%N A051873 21-gonal numbers: a(n) = n*(19n - 17)/2.
%C A051873 Sequence found by reading the line from 0, in the direction 0, 21, ... and the parallel line from 1, in the direction 1, 60, ..., in the square spiral whose vertices are the generalized 21-gonal numbers. - _Omar E. Pol_, Jul 18 2012
%C A051873 Partial sums of A215144. - _Leo Tavares_, Mar 17 2023
%D A051873 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
%D A051873 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
%H A051873 Vincenzo Librandi, <a href="/A051873/b051873.txt">Table of n, a(n) for n = 0..1000</a>
%H A051873 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A051873 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A051873 G.f.: x*(1+18*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011
%F A051873 a(n) = 19*n+a(n-1)-18 with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 06 2010
%F A051873 a(n) = A226490(n) - n. - _Bruno Berselli_, Jun 11 2013
%F A051873 a(19*a(n)+172*n+1) = a(19*a(n)+172*n) + a(19*n+1). - _Vladimir Shevelev_, Jan 24 2014
%F A051873 Product_{n>=2} (1 - 1/a(n)) = 19/21. - _Amiram Eldar_, Jan 22 2021
%F A051873 E.g.f.: exp(x)*(x + 19*x^2/2). - _Nikolaos Pantelidis_, Feb 06 2023
%p A051873 A051873 := proc(n) n*(19*n-17)/2 ;end proc: seq(A051873(n),n=0..30) ; # _R. J. Mathar_, Feb 05 2011
%t A051873 PolygonalNumber[21,Range[0,40]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 22 2016 *)
%t A051873 Table[n*(19*n - 17)/2, {n, 0, 100}] (* _Robert Price_, Oct 11 2018 *)
%o A051873 (PARI) n*(19*n-17)/2 \\ _Charles R Greathouse IV_, Jan 24 2014
%Y A051873 Cf. A215144, A226490.
%K A051873 nonn,easy
%O A051873 0,3
%A A051873 _N. J. A. Sloane_, Dec 15 1999

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