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A155753 a(n) = (n^3 - n + 9)/3.

%I A155753 #25 Jun 06 2021 07:28:09
%S A155753 3,5,11,23,43,73,115,171,243,333,443,575,731,913,1123,1363,1635,1941,
%T A155753 2283,2663,3083,3545,4051,4603,5203,5853,6555,7311,8123,8993,9923,
%U A155753 10915,11971,13093,14283,15543,16875,18281,19763,21323,22963
%N A155753 a(n) = (n^3 - n + 9)/3.
%H A155753 Bruno Berselli, <a href="/A155753/b155753.txt">Table of n, a(n) for n = 1..10000</a>.
%H A155753 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A155753 a(n) = a(n-1) + n*(n-1), with a(1)=3 .
%F A155753 From _Bruno Berselli_, Jun 21 2010: (Start)
%F A155753 G.f.: x*(3 -9*x +11*x^2 -3*x^3)/(1-x)^4.
%F A155753 a(n) + a(n-1) = 2*A153057(n-1) (n>1).
%F A155753 a(n) + A000217(n) = A153057(n) (n>0).
%F A155753 a(n) - 4*a(n-1) + 6*a(n-2) - 4*a(n-3) + a(n-4) = 0 with n>4.
%F A155753 a(n) = 3 + A007290(n+1) = (n^3 - n + 9)/3. (End)
%F A155753 E.g.f.: (1/3)*(-9 + (9 + 3*x^2 + x^3)*exp(x)). - _G. C. Greubel_, Jun 05 2021
%t A155753 f[n_]:=(n^3 -n +9)/3; f[Range[1,100]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2011*)
%t A155753 LinearRecurrence[{4,-6,4,-1}, {3,5,11,23}, 50] (* _Harvey P. Dale_, Oct 20 2011 *)
%o A155753 (PARI) a(n)=(n^3-n)/3+3 \\ _Charles R Greathouse IV_, Jan 11 2012
%o A155753 (Sage) [(n^3 -n +9)/3 for n in (1..50)] # _G. C. Greubel_, Jun 05 2021
%Y A155753 Cf. A000217, A007290, A153057.
%K A155753 nonn,easy
%O A155753 1,1
%A A155753 _Vincenzo Librandi_, Jan 26 2009
%E A155753 Entries confirmed by _John W. Layman_, Jun 17 2010
%E A155753 Edited by _Bruno Berselli_, Aug 12 2010
%E A155753 New name from _Charles R Greathouse IV_, Jan 11 2012