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%I #29 Feb 03 2021 09:00:39
%S 0,15,60,135,240,375,540,735,960,1215,1500,1815,2160,2535,2940,3375,
%T 3840,4335,4860,5415,6000,6615,7260,7935,8640,9375,10140,10935,11760,
%U 12615,13500,14415,15360,16335,17340,18375,19440,20535,21660,22815
%N a(n) = 15*n^2.
%C Number of edges in a complete 6-partite graph of order 6n, K_n,n,n,n,n,n.
%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)*15 = A033428(n)*5 = A033429(n)*3. - _Omar E. Pol_, Dec 13 2008
%F a(n) = A008587(n)*A008585(n). - _Reinhard Zumkeller_, Apr 12 2010
%F a(n) = a(n-1) + 30*n - 15 for n>0, a(0)=0. - _Vincenzo Librandi_, Dec 15 2010
%F a(n) = A022272(n) + A022272(-n). - _Bruno Berselli_, Mar 31 2015
%F a(n) = t(6*n) - 6*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(6*n) - 6*A000217(n). - _Bruno Berselli_, Aug 31 2017
%F From _Amiram Eldar_, Feb 03 2021: (Start)
%F Sum_{n>=1} 1/a(n) = Pi^2/90.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/180.
%F Product_{n>=1} (1 + 1/a(n)) = sqrt(15)*sinh(Pi/sqrt(15))/Pi.
%F Product_{n>=1} (1 - 1/a(n)) = sqrt(15)*sin(Pi/sqrt(15))/Pi. (End)
%t Table[15*n^2, {n, 0, 45}] (* _Amiram Eldar_, Feb 03 2021 *)
%o (PARI) a(n)=15*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000217, A000290, A008585, A008587, A022272, A033428, A033581, A033583, A033429.
%K nonn,easy
%O 0,2
%A _Roberto E. Martinez II_, Oct 18 2001
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