A017199 - OEIS

%I #23 Oct 03 2024 03:46:25

%S 27,1728,9261,27000,59319,110592,185193,287496,421875,592704,804357,

%T 1061208,1367631,1728000,2146689,2628072,3176523,3796416,4492125,

%U 5268024,6128487,7077888,8120601,9261000,10503459,11852352,13312053,14886936,16581375,18399744,20346417

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

%H Vincenzo Librandi, <a href="/A017199/b017199.txt">Table of n, a(n) for n = 0..10000</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.: 27*(1 + 60*x + 93*x^2 + 8*x^3)/ (x-1)^4. - _R. J. Mathar_, Aug 01 2014

%F a(n) = 27*A016779(n). - _R. J. Mathar_, Aug 01 2014

%F From _Amiram Eldar_, Oct 03 2024: (Start)

%F a(n) = A017197(n)^3.

%F Sum_{n>=0} 1/a(n) = 2*Pi^3/(2187*sqrt(3)) + 13*zeta(3)/729. (End)

%t (9Range[0,30]+3)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{27,1728,9261,27000},30] (* _Harvey P. Dale_, Jun 20 2024 *)

%o (Magma) [(9*n+3)^3: n in [0..30]]; // _Vincenzo Librandi_, Jul 23 2011

%Y Cf. A002117, A016779, A017197.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_