A244729 - OEIS

%I #10 Sep 08 2022 08:46:08

%S 0,10,80,270,640,1250,2160,3430,5120,7290,10000,13310,17280,21970,

%T 27440,33750,40960,49130,58320,68590,80000,92610,106480,121670,138240,

%U 156250,175760,196830,219520,243890,270000,297910,327680,359370,393040,428750,466560

%N 10*n^3.

%H Vincenzo Librandi, <a href="/A244729/b244729.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.: 10*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.

%t Table[10 n^3, {n, 0, 40}] (* or *) CoefficientList[Series[10 x (1 + 4 x + x^2)/(1 - x)^4, {x, 0, 40}], x]

%o (Magma) [10*n^3: n in [0..40]] /* or */ I:=[0,10,80,270]; [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. similar sequences listed in A244725.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jul 05 2014