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%I #27 Feb 19 2024 03:04:28
%S 0,1,9,134,1862,26251,369251,5196060,73113372,1028784997,14476099149,
%T 203694183170,2866194639170,40330419190351,567492063162119,
%U 7985219303802744,112360562315573112,1581033091723823881,22246823846444284881,313036566941955454910
%N a(n) = Sum_{i=0..n} A000129(i)^3.
%H Bruno Berselli, <a href="/A213688/b213688.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,18,-42,11,1).
%F G.f.: x*(1-4*x-x^2)/((1-x)*(1+2*x-x^2)*(1-14*x-x^2)). [_Bruno Berselli_, Jun 18 2012]
%F a(n) = ((3+sqrt(2))*(1+sqrt(2))^(3n+1)+(3-sqrt(2))*(1-sqrt(2))^(3n+1)-21*(-1)^n*((1+sqrt(2))^n+(1-sqrt(2))^n)+32)/224. [_Bruno Berselli_, Jun 18 2012]
%t LinearRecurrence[{13, 18, -42, 11, 1}, {0, 1, 9, 134, 1862}, 20] (* _Bruno Berselli_, Jun 21 2012 *)
%o (Magma) A110272:=func<n | n le 3 select Ceiling(n^2/2)^3 else 12*Self(n)+30*Self(n-1)-12*Self(n-2)-Self(n-3)>; [&+[A110272(i): i in [0..n]]: n in [0..19]]; // _Bruno Berselli_, Jun 21 2012
%Y Cf. A000129, A048739 (partial sums of A000129), A084158 (sum of squares of A000129).
%Y Cf. A110272 (cubes of the Pell numbers).
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 18 2012
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