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%I #30 Feb 03 2021 07:46:23
%S 0,7,28,63,112,175,252,343,448,567,700,847,1008,1183,1372,1575,1792,
%T 2023,2268,2527,2800,3087,3388,3703,4032,4375,4732,5103,5488,5887,
%U 6300,6727,7168,7623,8092,8575,9072,9583,10108,10647,11200,11767,12348,12943,13552,14175
%N a(n) = 7*n^2.
%C Number of edges of the complete bipartite graph of order 8n, K_n,7n - _Roberto E. Martinez II_, Jan 07 2002
%C Number of edges of the complete tripartite graph of order 5n, K_n,n,3n - _Roberto E. Martinez II_, Jan 07 2002
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F Central terms of the triangle in A132111: a(n) = A132111(2*n, n). - _Reinhard Zumkeller_, Aug 10 2007
%F a(n) = 7 * A000290(n). - _Omar E. Pol_, Dec 11 2008
%F a(n) = 14*n + a(n-1) - 7 (with a(0) = 0). - _Vincenzo Librandi_, Aug 05 2010
%F G.f.: -7*x*(1+x)/(x-1)^3 . - _R. J. Mathar_, Feb 06 2017
%F From _Amiram Eldar_, Feb 03 2021: (Start)
%F Sum_{n>=1} 1/a(n) = Pi^2/42.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/84.
%F Product_{n>=1} (1 + 1/a(n)) = sqrt(7)*sinh(Pi/sqrt(7))/Pi.
%F Product_{n>=1} (1 - 1/a(n)) = sqrt(7)*sin(Pi/sqrt(7))/Pi. (End)
%t 7Range[0, 49]^2 (* _Alonso del Arte_, Jun 30 2013 *)
%o (PARI) a(n)=7*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000290, A132111.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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