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A033584 a(n) = 11*n^2.

%I A033584 #22 Nov 30 2024 00:35:09
%S A033584 0,11,44,99,176,275,396,539,704,891,1100,1331,1584,1859,2156,2475,
%T A033584 2816,3179,3564,3971,4400,4851,5324,5819,6336,6875,7436,8019,8624,
%U A033584 9251,9900,10571,11264,11979,12716
%N A033584 a(n) = 11*n^2.
%C A033584 From _Roberto E. Martinez II_, Jan 07 2002: (Start)
%C A033584 Number of edges of the complete tripartite graph of order 7n, K_n,n,5n.
%C A033584 Number of edges of the complete tripartite graph of order 6n, K_n,2n,3n. (End)
%C A033584 11 times the squares. - _Omar E. Pol_, Dec 13 2008
%H A033584 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A033584 a(n) = 11*A000290(n). - _Omar E. Pol_, Dec 13 2008
%F A033584 a(n) = 22*n + a(n-1) - 11 (with a(0)=0). - _Vincenzo Librandi_, Aug 05 2010
%F A033584 From _Amiram Eldar_, Feb 03 2021: (Start)
%F A033584 Sum_{n>=1} 1/a(n) = Pi^2/66.
%F A033584 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/132.
%F A033584 Product_{n>=1} (1 + 1/a(n)) = sqrt(11)*sinh(Pi/sqrt(11))/Pi.
%F A033584 Product_{n>=1} (1 - 1/a(n)) = sqrt(11)*sin(Pi/sqrt(11))/Pi. (End)
%F A033584 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A033584 G.f.: 11*x*(1 + x)/(1-x)^3.
%F A033584 E.g.f.: 11*x*(1 + x)*exp(x).
%F A033584 a(n) = n*A008593(n) = A195043(2*n).
%F A033584 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%e A033584 a(1)=22*1+0-11=11; a(2)=22*2+11-11=44; a(3)=22*3+44-11=99 - _Vincenzo Librandi_, Aug 05 2010
%t A033584 Table[11*n^2, {n, 0, 35}] (* _Amiram Eldar_, Feb 03 2021 *)
%o A033584 (PARI) a(n)=11*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A033584 Cf. A000290, A008593, A195043.
%K A033584 nonn,easy
%O A033584 0,2
%A A033584 _N. J. A. Sloane_