A244728 - OEIS

%I #30 Sep 08 2022 08:46:08

%S 0,9,72,243,576,1125,1944,3087,4608,6561,9000,11979,15552,19773,24696,

%T 30375,36864,44217,52488,61731,72000,83349,95832,109503,124416,140625,

%U 158184,177147,197568,219501,243000,268119,294912,323433,353736,385875,419904

%N a(n) = 9*n^3.

%C Volume of a pyramid (square base) with side and height 3*n. - _Wesley Ivan Hurt_, Aug 25 2014

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

%H Vincenzo Librandi, <a href="/A244728/b244728.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

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

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

%F E.g.f.: 9*x*(1 + 3*x + x^2)*exp(x). - _G. C. Greubel_, Jun 30 2019

%p A244728:=n->9*n^3: seq(A244728(n), n=0..40); # _Wesley Ivan Hurt_, Aug 25 2014

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

%o (Magma) [9*n^3: n in [0..40]] /* or */ 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]];

%o (PARI) vector(40, n, n--; 9*n^3) \\ _G. C. Greubel_, Jun 30 2019

%o (Sage) [9*n^3 for n in (0..40)] # _G. C. Greubel_, Jun 30 2019

%o (GAP) List([0..40], n-> 9*n^3) # _G. C. Greubel_, Jun 30 2019

%Y Cf. similar sequences listed in A244725.

%Y Cf. A287335 (see Crossrefs).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jul 05 2014