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a(n) = 11*n^2.
9

%I #18 Feb 03 2021 09:02:24

%S 0,11,44,99,176,275,396,539,704,891,1100,1331,1584,1859,2156,2475,

%T 2816,3179,3564,3971,4400,4851,5324,5819,6336,6875,7436,8019,8624,

%U 9251,9900,10571,11264,11979,12716

%N a(n) = 11*n^2.

%C Number of edges of the complete tripartite graph of order 7n, K_n,n,5n - _Roberto E. Martinez II_, Jan 07 2002

%C Number of edges of the complete tripartite graph of order 6n, K_n,2n,3n - _Roberto E. Martinez II_, Jan 07 2002

%C 11 times the squares. - _Omar E. Pol_, Dec 13 2008

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = A000290(n)*11. - _Omar E. Pol_, Dec 13 2008

%F a(n) = 22*n+a(n-1)-11 (with a(0)=0) - _Vincenzo Librandi_, Aug 05 2010

%F From _Amiram Eldar_, Feb 03 2021: (Start)

%F Sum_{n>=1} 1/a(n) = Pi^2/66.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/132.

%F Product_{n>=1} (1 + 1/a(n)) = sqrt(11)*sinh(Pi/sqrt(11))/Pi.

%F Product_{n>=1} (1 - 1/a(n)) = sqrt(11)*sin(Pi/sqrt(11))/Pi. (End)

%e 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 Table[11*n^2, {n, 0, 35}] (* _Amiram Eldar_, Feb 03 2021 *)

%o (PARI) a(n)=11*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000290.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.