A244728 a(n) = 9*n^3.

0, 9, 72, 243, 576, 1125, 1944, 3087, 4608, 6561, 9000, 11979, 15552, 19773, 24696, 30375, 36864, 44217, 52488, 61731, 72000, 83349, 95832, 109503, 124416, 140625, 158184, 177147, 197568, 219501, 243000, 268119, 294912, 323433, 353736, 385875, 419904

Offset: 0

Author

Vincenzo Librandi, Jul 05 2014

Keywords

• nonn
• easy

Comments

Volume of a pyramid (square base) with side and height 3*n. - Wesley Ivan Hurt, Aug 25 2014

Volume of the smallest square cuboid containing a ring torus where the tube and hole diameters are both n. - Torlach Rush, Jun 04 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. similar sequences listed in A244725.

Cf. A287335 (see Crossrefs).

Programs

GAP

List([0..40], n-> 9*n^3); # G. C. Greubel, Jun 30 2019

Magma

[9*n^3: n in [0..40]];

Magma

I:=[0,9,72,243]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]];

Maple

A244728:=n->9*n^3: seq(A244728(n), n=0..40); # Wesley Ivan Hurt, Aug 25 2014

Mathematica

Table[9n^3, {n,0,40}] (* or *) CoefficientList[Series[9*x*(1+4*x+x^2)/(1- x)^4, {x,0,40}], x]

PARI

vector(40, n, n--; 9*n^3) \\ G. C. Greubel, Jun 30 2019

Sage

[9*n^3 for n in (0..40)] # G. C. Greubel, Jun 30 2019

Formula

G.f.: 9*x*(1 + 4*x + x^2)/(1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.

E.g.f.: 9*x*(1 + 3*x + x^2)*exp(x). - G. C. Greubel, Jun 30 2019