A244727 - OEIS

%I #23 Apr 04 2024 11:04:39

%S 0,7,56,189,448,875,1512,2401,3584,5103,7000,9317,12096,15379,19208,

%T 23625,28672,34391,40824,48013,56000,64827,74536,85169,96768,109375,

%U 123032,137781,153664,170723,189000,208537,229376,251559,275128,300125,326592,354571,384104

%N a(n) = 7*n^3.

%C After 0, subsequence of A038855.

%C Volume of a truncated square pyramid with base lengths n and 2n, and height 3n. - _Wesley Ivan Hurt_, Apr 05 2016

%H Vincenzo Librandi, <a href="/A244727/b244727.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.: 7*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.: 7*exp(x)*x*(1 + 3*x + x^2). - _Stefano Spezia_, May 09 2023

%p A244727:=n->7*n^3: seq(A244727(n), n=0..100); # _Wesley Ivan Hurt_, Apr 05 2016

%t Table[7 n^3, {n, 0, 40}] (* or *) CoefficientList[Series[7 x (1 + 4 x + x^2)/(1 - x)^4, {x, 0, 40}], x]

%t 7 Range[0, 50]^3 (* _Wesley Ivan Hurt_, Apr 05 2016 *)

%t LinearRecurrence[{4,-6,4,-1},{0,7,56,189},40] (* _Harvey P. Dale_, Apr 04 2024 *)

%o (Magma) [7*n^3: n in [0..40]] /* or */ I:=[0,7,56,189]; [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]];

%Y Cf. A038855.

%Y Cf. similar sequences listed in A244725.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jul 05 2014