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A216243 Partial sums of the squares of Lucas numbers (A000032). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

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 *)

CROSSREFS

Cf. A001654.

Sequence in context: A350527 A316415 A007084 * A093862 A041375 A042279

Adjacent sequences: A216240 A216241 A216242 * A216244 A216245 A216246

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Mar 14 2013

STATUS

approved

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Last modified February 6 17:09 EST 2023. Contains 360110 sequences. (Running on oeis4.)