cp's OEIS Frontend

A244725 a(n) = 5*n^3.

%I A244725 #18 Jun 15 2025 18:23:16
%S A244725 0,5,40,135,320,625,1080,1715,2560,3645,5000,6655,8640,10985,13720,
%T A244725 16875,20480,24565,29160,34295,40000,46305,53240,60835,69120,78125,
%U A244725 87880,98415,109760,121945,135000,148955,163840,179685,196520,214375,233280,253265
%N A244725 a(n) = 5*n^3.
%H A244725 Vincenzo Librandi, <a href="/A244725/b244725.txt">Table of n, a(n) for n = 0..1000</a>
%H A244725 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A244725 G.f.: 5*x*(1 + 4*x + x^2)/(1 - x)^4.
%F A244725 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.
%t A244725 Table[5 n^3, {n, 0, 40}] (* or *) CoefficientList[Series[5 x (1 + 4 x + x^2)/(1 - x)^4, {x, 0, 40}], x]
%o A244725 (Magma) [5*n^3: n in [0..40]];
%o A244725 (Magma) I:=[0,5,40,135]; [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 A244725 (PARI) a(n)=5*n^3 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A244725 Cf. similar sequences of the type k*n^3: A000578 (k=1), A033431 (k=2), A117642  (k=3), A033430 (k=4), this sequence (k=5), A244726 (k=6), A244727 (k=7), A016743 (k=8), A244728 (k=9), A244729 (k=10), A016767 (k=27), A016803 (k=64),  A016851 (k=125), A016911 (k=216), A016983 (k=343), A017067 (k=512),  A017163 (k=729), A017271 (k=1000), A017391 (k=1331), A017523 (k=1728).
%K A244725 nonn,easy
%O A244725 0,2
%A A244725 _Vincenzo Librandi_, Jul 05 2014