login
a(n) = (3*n)^3.
8

%I #29 Sep 08 2022 08:44:41

%S 0,27,216,729,1728,3375,5832,9261,13824,19683,27000,35937,46656,59319,

%T 74088,91125,110592,132651,157464,185193,216000,250047,287496,328509,

%U 373248,421875,474552,531441,592704

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

%H Vincenzo Librandi, <a href="/A016767/b016767.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F From _Reinhard Zumkeller_, Jan 29 2009: (Start)

%F a(n) = 27*A000578(n).

%F A020639(a(n)) = A010693(n), for n>0. (End)

%F a(n) = A155955(n,3) for n>2. - _Reinhard Zumkeller_, Jan 31 2009

%F G.f.: 27*x*(1+4*x+x^2)/(x-1)^4 . - _R. J. Mathar_, Jul 07 2017

%F E.g.f.: 27*x*(1 + 3*x + x^2)*exp(x). - _G. C. Greubel_, Sep 15 2018

%F a(n) = -a(-n) for all n in Z. - _Michael Somos_, Sep 16 2018

%e G.f. = 27*x + 216*x^2 + 729*x^3 * 1728*x^4 + 3375*x^5 + 5832*x^6 + ... - _Michael Somos_, Sep 16 2018

%t Table[(3*n)^3, {n,0,30}] (* _G. C. Greubel_, Sep 15 2018 *)

%o (Magma) [(3*n)^3: n in [0..40]]; // _Vincenzo Librandi_, Jul 29 2011

%o (PARI) a(n)=27*n^3 \\ _Charles R Greathouse IV_, Jul 29 2011

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_