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A254371 Sum of cubes of the first n even numbers (A016743). 1
0, 8, 72, 288, 800, 1800, 3528, 6272, 10368, 16200, 24200, 34848, 48672, 66248, 88200, 115200, 147968, 187272, 233928, 288800, 352800, 426888, 512072, 609408, 720000, 845000, 985608, 1143072, 1318688, 1513800, 1729800, 1968128, 2230272, 2517768, 2832200, 3175200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Luciano Ancora, The Square Pyramidal Number and other figurate numbers, ch. 3.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

G.f.: 8*x*(1 + 4*x + x^2)/(1 - x)^5.

a(n) = 2*n^2*(n + 1)^2.

a(n) = 2*A035287(n+1) = 2*A002378(n)^2 = 8*A000217(n)^2. - Bruce J. Nicholson, Apr 23 2017

a(n) = 8*A000537(n). - Michel Marcus, Apr 23 2017

MAPLE

A254371:=n->2*n^2*(n + 1)^2: seq(A254371(n), n=0..50); # Wesley Ivan Hurt, Apr 28 2017

MATHEMATICA

Table[2 n^2 (n+1)^2, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 8, 72, 288, 800}, 40]

Accumulate[Range[0, 80, 2]^3] (* Harvey P. Dale, Jun 26 2017 *)

PROG

(PARI) a(n)=sum(i=0, n, 8*i^3); \\ Michael B. Porter, Mar 16 2015

(MAGMA) [2*n^2*(n+1)^2: n in [0..40]]; // Bruno Berselli, Mar 23 2015

(GAP) List([0..35], n->2*(n*(n+1))^2); # Muniru A Asiru, Oct 24 2018

CROSSREFS

Cf. A000537 (sum of first n cubes); A002593 (sum of first n odd cubes).

Cf. A060300 (2*a(n)).

First bisection of A105636; second bisection of A212892.

Cf. A000217, A002378, A035287.

Sequence in context: A064015 A044576 A104453 * A143945 A239095 A189954

Adjacent sequences:  A254368 A254369 A254370 * A254372 A254373 A254374

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Mar 16 2015

STATUS

approved

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Last modified July 19 12:35 EDT 2019. Contains 325159 sequences. (Running on oeis4.)