A016956 - OEIS

%I #16 Mar 31 2022 03:12:17

%S 531441,282429536481,129746337890625,7355827511386641,

%T 150094635296999121,1667889514952984961,12381557655576425121,

%U 68952523554931640625,309629344375621415601,1176246293903439668001,3909188328478827879681,11646329922777311412561,31676352024078369140625

%N a(n) = (6*n + 3)^12.

%H Vincenzo Librandi, <a href="/A016956/b016956.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F From _Amiram Eldar_, Mar 31 2022: (Start)

%F a(n) = A016945(n)^12 = A016946(n)^6 = A016947(n)^4 = A016948(n)^3 = A016950(n)^2..

%F a(n) = 3^12*A016764(n).

%F Sum_{n>=0} 1/a(n) = 691*Pi^12/339414785740800. (End)

%t (6*Range[0,20]+3)^12 (* _Harvey P. Dale_, Jan 23 2013 *)

%o (Magma) [(6*n+3)^12: n in [0..20]]; // _Vincenzo Librandi_, May 06 2011

%Y Cf. A016764, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953, A016954, A016955.

%Y Subsequence of A008456.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_