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A051876 24-gonal numbers: a(n) = n*(11*n-10).

%I A051876 #56 Feb 05 2023 15:06:14
%S A051876 0,1,24,69,136,225,336,469,624,801,1000,1221,1464,1729,2016,2325,2656,
%T A051876 3009,3384,3781,4200,4641,5104,5589,6096,6625,7176,7749,8344,8961,
%U A051876 9600,10261,10944,11649,12376,13125,13896,14689,15504,16341
%N A051876 24-gonal numbers: a(n) = n*(11*n-10).
%C A051876 Sequence found by reading the line from 0, in the direction 0, 24,... and the parallel line from 1, in the direction 1, 69,..., in the square spiral whose vertices are the generalized 24-gonal numbers. - _Omar E. Pol_, Jul 18 2012
%C A051876 This is also a star dodecagonal number: a(n) = A051624(n) + 12*A000217(n-1). - _Luciano Ancora_, Mar 30 2015
%D A051876 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
%D A051876 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
%H A051876 Ivan Panchenko, <a href="/A051876/b051876.txt">Table of n, a(n) for n = 0..1000</a>
%H A051876 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A051876 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A051876 a(n) = 22*n+a(n-1)-21, with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 06 2010
%F A051876 G.f.: x*(1+21*x)/(1-x)^3. - _Colin Barker_, Jan 10 2012
%F A051876 a(22*a(n)+232*n+1) = a(22*a(n)+232*n) + a(22*n+1). - _Vladimir Shevelev_, Jan 24 2014
%F A051876 Product_{n>=2} (1 - 1/a(n)) = 11/12. - _Amiram Eldar_, Jan 22 2021
%F A051876 E.g.f.: exp(x)*(x + 11*x^2). - _Nikolaos Pantelidis_, Feb 05 2023
%p A051876 A051876:=n->n*(11*n - 10); seq(A051876(n), n=0..50); # _Wesley Ivan Hurt_, Feb 25 2014
%t A051876 Table[n (11 n - 10), {n, 0, 50}] (* _Wesley Ivan Hurt_, Feb 25 2014 *)
%o A051876 (PARI) a(n)=n*(11*n-10) \\ _Charles R Greathouse IV_, Jul 19 2011
%K A051876 nonn,easy
%O A051876 0,3
%A A051876 _N. J. A. Sloane_, Dec 15 1999