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A216243 Partial sums of the squares of Lucas numbers (A000032).

%I A216243 #18 Jan 26 2021 16:05:10
%S A216243 4,5,14,30,79,200,524,1365,3574,9350,24479,64080,167764,439205,
%T A216243 1149854,3010350,7881199,20633240,54018524,141422325,370248454,
%U A216243 969323030,2537720639,6643838880,17393796004,45537549125,119218851374,312119004990,817138163599,2139295485800
%N A216243 Partial sums of the squares of Lucas numbers (A000032).
%H A216243 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,1).
%F A216243 a(n) = Sum_{i=0..n} A001254(i) = A002878(n) +A176040(n) = A215602(n)+2.
%F A216243 G.f.: ( -4+7*x+x^2 ) / ( (x-1)*(1+x)*(x^2-3*x+1) ).
%F A216243 a(n) = -7*A064831(n) -A064831(n-1) +4*A064831(n+1).
%F A216243 a(n) = L(2*n+1) + 2 + (-1)^n, for L(n) the Lucas sequence A000032(n). - _Greg Dresden_, Jan 26 2021
%p A216243 A001254 := proc(n)
%p A216243         A000032(n)^2 ;
%p A216243 end proc;
%p A216243 A := proc(n)
%p A216243         add( A001254(i),i=0..n) ;
%p A216243 end proc:
%t A216243 Accumulate[LucasL[Range[0,30]]^2] (* or *) LinearRecurrence[{3,0,-3,1},{4,5,14,30},30] (* _Harvey P. Dale_, Oct 13 2019 *)
%Y A216243 Cf. A001654.
%K A216243 nonn,easy
%O A216243 0,1
%A A216243 _R. J. Mathar_, Mar 14 2013