|
%I #16 Sep 08 2022 08:46:02
%S 1,12,40,96,187,324,514,768,1093,1500,1996,2592,3295,4116,5062,6144,
%T 7369,8748,10288,12000,13891,15972,18250,20736,23437,26364,29524,
%U 32928,36583,40500,44686,49152,53905,58956,64312,69984,75979,82308
%N n^3 + floor(n^3/2).
%C Row 2 of the array A211785.
%H Bruno Berselli, <a href="/A211786/b211786.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -2, 3, -1).
%F a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F G.f.: x*(1+9*x+6*x^2+2*x^3)/((1+x)*(1-x)^4). [_Bruno Berselli_, May 06 2012]
%F a(n) = floor(3*n^3/2) = (6*n^3+(-1)^n-1)/4. [_Bruno Berselli_, May 06 2012]
%t f[n_, m_] := Sum[Floor[n^3/k], {k, 1, m}]
%t t = Table[f[n, 2], {n, 1, 90}]
%t FindLinearRecurrence[t]
%t LinearRecurrence[{3, -2, -2, 3, -1},{1, 12, 40, 96, 187},38] (* _Ray Chandler_, Aug 02 2015 *)
%o (Magma) [n^3+Floor(n^3/2): n in [1..38]]; // _Bruno Berselli_, May 06 2012
%Y Cf. A032766 (n+floor(n/2)), A032528 (n^2+floor(n^2/2)), A211701.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Apr 20 2012
|
