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

%I A244728 #33 Jun 15 2025 18:27:20
%S A244728 0,9,72,243,576,1125,1944,3087,4608,6561,9000,11979,15552,19773,24696,
%T A244728 30375,36864,44217,52488,61731,72000,83349,95832,109503,124416,140625,
%U A244728 158184,177147,197568,219501,243000,268119,294912,323433,353736,385875,419904
%N A244728 a(n) = 9*n^3.
%C A244728 Volume of a pyramid (square base) with side and height 3*n. - _Wesley Ivan Hurt_, Aug 25 2014
%C A244728 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 A244728 Vincenzo Librandi, <a href="/A244728/b244728.txt">Table of n, a(n) for n = 0..1000</a>
%H A244728 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A244728 G.f.: 9*x*(1 + 4*x + x^2)/(1 - x)^4.
%F A244728 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.
%F A244728 E.g.f.: 9*x*(1 + 3*x + x^2)*exp(x). - _G. C. Greubel_, Jun 30 2019
%p A244728 A244728:=n->9*n^3: seq(A244728(n), n=0..40); # _Wesley Ivan Hurt_, Aug 25 2014
%t A244728 Table[9n^3, {n,0,40}] (* or *) CoefficientList[Series[9*x*(1+4*x+x^2)/(1- x)^4, {x,0,40}], x]
%o A244728 (Magma) [9*n^3: n in [0..40]];
%o A244728 (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]];
%o A244728 (PARI) vector(40, n, n--; 9*n^3) \\ _G. C. Greubel_, Jun 30 2019
%o A244728 (Sage) [9*n^3 for n in (0..40)] # _G. C. Greubel_, Jun 30 2019
%o A244728 (GAP) List([0..40], n-> 9*n^3); # _G. C. Greubel_, Jun 30 2019
%Y A244728 Cf. similar sequences listed in A244725.
%Y A244728 Cf. A287335 (see Crossrefs).
%K A244728 nonn,easy
%O A244728 0,2
%A A244728 _Vincenzo Librandi_, Jul 05 2014