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A118465 a(n) = 8*n^3 + n. 2
0, 9, 66, 219, 516, 1005, 1734, 2751, 4104, 5841, 8010, 10659, 13836, 17589, 21966, 27015, 32784, 39321, 46674, 54891, 64020, 74109, 85206, 97359, 110616, 125025, 140634, 157491, 175644, 195141, 216030, 238359, 262176, 287529, 314466, 343035 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(8*n^3 + n, 8*n^3 - n) solves the Diophantine equation 2*(X-Y)^3-(X+Y)=0.

(m*(2n)^k+n, m*(2n)^k-n) solves the Diophantine equation: 2m*(X-Y)^k-(X+Y)=0 with X>=Y,k>=2 and where m is a positive integer. Also ((m*n^k+n)/2, (m*n^k-n)/2) solves the Diophantine equation: m*(X-Y)^k-(X+Y)=0 with X>=Y,k>=2 where m is an odd number.

24*a(n) = (4n+1)^3 + (4n)^3 + (4n-1)^3. [Bruno Berselli, May 12 2014]

LINKS

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

FORMULA

G.f.: 3*x*(x+3)*(3*x+1)/(-1+x)^4. - R. J. Mathar, Nov 14 2007

a(n) = n*A081585(n). - Vincenzo Librandi, May 13 2014

MAPLE

A118465:=n->8*n^3 + n; seq(A118465(n), n=0..30); # Wesley Ivan Hurt, May 13 2014

MATHEMATICA

Table[8 n^3 + n, {n, 0, 35}]

CoefficientList[Series[3 x (x + 3) (3 x + 1)/(-1 + x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, May 13 2014 *)

PROG

(MAGMA) [8*n^3 + n: n in [0..30]]; // Wesley Ivan Hurt, May 13 2014

CROSSREFS

Cf. A006003, A081585.

Sequence in context: A120286 A152581 A122733 * A279129 A051375 A081902

Adjacent sequences:  A118462 A118463 A118464 * A118466 A118467 A118468

KEYWORD

nonn,easy

AUTHOR

Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 16 2006, Oct 02 2007

EXTENSIONS

Edited by Stefan Steinerberger, Jul 24 2007

STATUS

approved

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Last modified March 18 17:51 EDT 2019. Contains 321292 sequences. (Running on oeis4.)