cp's OEIS Frontend

A064761 a(n) = 15*n^2.

%I A064761 #33 Nov 30 2024 00:34:58
%S A064761 0,15,60,135,240,375,540,735,960,1215,1500,1815,2160,2535,2940,3375,
%T A064761 3840,4335,4860,5415,6000,6615,7260,7935,8640,9375,10140,10935,11760,
%U A064761 12615,13500,14415,15360,16335,17340,18375,19440,20535,21660,22815
%N A064761 a(n) = 15*n^2.
%C A064761 Number of edges in a complete 6-partite graph of order 6n, K_n,n,n,n,n,n.
%H A064761 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A064761 a(n) = 15*A000290(n) = 5*A033428(n) = 3*A033429(n). - _Omar E. Pol_, Dec 13 2008
%F A064761 a(n) = A008587(n)*A008585(n). - _Reinhard Zumkeller_, Apr 12 2010
%F A064761 a(n) = a(n-1) + 30*n - 15 for n > 0, a(0)=0. - _Vincenzo Librandi_, Dec 15 2010
%F A064761 a(n) = A022272(n) + A022272(-n). - _Bruno Berselli_, Mar 31 2015
%F A064761 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 A064761 From _Amiram Eldar_, Feb 03 2021: (Start)
%F A064761 Sum_{n>=1} 1/a(n) = Pi^2/90.
%F A064761 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/180.
%F A064761 Product_{n>=1} (1 + 1/a(n)) = sqrt(15)*sinh(Pi/sqrt(15))/Pi.
%F A064761 Product_{n>=1} (1 - 1/a(n)) = sqrt(15)*sin(Pi/sqrt(15))/Pi. (End)
%F A064761 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A064761 G.f.: 15*x*(1 + x)/(1 - x)^3.
%F A064761 E.g.f.: 15*x*(1 + x)*exp(x).
%F A064761 a(n) = n*A008597(n) = A195046(2*n).
%F A064761 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A064761 Table[15*n^2, {n, 0, 45}] (* _Amiram Eldar_, Feb 03 2021 *)
%o A064761 (PARI) a(n)=15*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A064761 Cf. A000217, A000290, A008585, A008587, A022272, A033428, A033429, A033581, A033583.
%Y A064761 Cf. A008597, A195046.
%K A064761 nonn,easy
%O A064761 0,2
%A A064761 _Roberto E. Martinez II_, Oct 18 2001