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

0,1

References

Ralph P. Grimaldi, Fibonacci and Catalan Numbers: An Introduction, (2012). See Exercise 11 at p. 98.

Links

Table of n, a(n) for n=0..29.

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

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

a(n) = L(n)*L(n+1) + 2 (see Grimaldi). - Stefano Spezia, Nov 20 2025

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] (* Harvey P. Dale, Oct 13 2019 *)
(* Alternative: *)
LinearRecurrence[{3, 0, -3, 1}, {4, 5, 14, 30}, 30] (* Harvey P. Dale, Oct 13 2019 *)

Crossrefs

Cf. A000032, A001254, A001654, A002878, A064831, A176040, A215602.

Sequence in context: A350527 A316415 A007084 * A093862 A041375 A042279

Adjacent sequences: A216240 A216241 A216242 * A216244 A216245 A216246

Keyword

nonn,easy,changed

Author

R. J. Mathar, Mar 14 2013

Status

approved