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%I A140681 #36 May 03 2023 18:45:09
%S A140681 0,21,48,81,120,165,216,273,336,405,480,561,648,741,840,945,1056,1173,
%T A140681 1296,1425,1560,1701,1848,2001,2160,2325,2496,2673,2856,3045,3240,
%U A140681 3441,3648,3861,4080,4305,4536,4773,5016,5265,5520,5781
%N A140681 a(n) = 3*n*(n+6).
%H A140681 G. C. Greubel, <a href="/A140681/b140681.txt">Table of n, a(n) for n = 0..5000</a>
%H A140681 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A140681 a(n) = A028560(n)*3 = 3*n^2 + 18*n = n*(3*n+18).
%F A140681 a(n) = 6*n + a(n-1) + 15 with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A140681 from _G. C. Greubel_, Jul 20 2017: (Start)
%F A140681 G.f.: 3*x*(7 - 5*x)/(1-x)^3.
%F A140681 E.g.f.: 3*x*(x+7)*exp(x). (End)
%F A140681 From _Amiram Eldar_, Feb 26 2022: (Start)
%F A140681 Sum_{n>=1} 1/a(n) = 49/360.
%F A140681 Sum_{n>=1} (-1)^(n+1)/a(n) = 37/1080. (End)
%p A140681 A140681:=n->3*n*(n+6); seq(A140681(n), n=0..100); # _Wesley Ivan Hurt_, Dec 10 2013
%t A140681 Table[3n(n+6), {n,0,100}] (* _Wesley Ivan Hurt_, Dec 10 2013 *)
%t A140681 LinearRecurrence[{3,-3,1},{0,21,48},50] (* _Harvey P. Dale_, May 03 2023 *)
%o A140681 (PARI) a(n)=3*n*(n+6) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A140681 Cf. A028560, A033428, A045944, A140676, A067725, A140677, A140678, A067707, A140679, A140680, A140689, A000217, A005563, A067728, A140091, A212331.
%K A140681 nonn,easy
%O A140681 0,2
%A A140681 _Omar E. Pol_, May 22 2008

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