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

4, 5, 14, 30, 79, 200, 524, 1365, 3574, 9350, 24479, 64080, 167764, 439205, 1149854, 3010350, 7881199, 20633240, 54018524, 141422325, 370248454, 969323030, 2537720639, 6643838880, 17393796004, 45537549125, 119218851374, 312119004990, 817138163599, 2139295485800

Offset: 0

Author

R. J. Mathar, Mar 14 2013

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).

Crossrefs

Cf. A001654.

Programs

Maple

A001254 := proc(n)
        A000032(n)^2 ;
end proc;
A := proc(n)
        add( A001254(i),i=0..n) ;
end proc:

Mathematica

Accumulate[LucasL[Range[0,30]]^2] (* or *) LinearRecurrence[{3,0,-3,1},{4,5,14,30},30] (* Harvey P. Dale, Oct 13 2019 *)

Formula

a(n) = Sum_{i=0..n} A001254(i) = A002878(n) +A176040(n) = A215602(n)+2.

G.f.: ( -4+7*x+x^2 ) / ( (x-1)*(1+x)*(x^2-3*x+1) ).

a(n) = -7*A064831(n) -A064831(n-1) +4*A064831(n+1).

a(n) = L(2*n+1) + 2 + (-1)^n, for L(n) the Lucas sequence A000032(n). - Greg Dresden, Jan 26 2021