A220509 - OEIS

%I #19 Sep 08 2022 08:46:04

%S 1,7,23,63,157,383,963,2551,7097,20439,60079,178511,533205,1596559,

%T 4785755,14352327,43050865,129145127,387426375,1162268383,3486792461,

%U 10460362527,31381070323,94143191063,282429550377,847288625143,2541865845983,7625597504751

%N n^3 + 3n + 3^n.

%C This is to A220425 as 3 is to 2.

%C The subsequence of primes begins: 7, 23, 157, 383, 2551, see A220701 for the associated n.

%H Vincenzo Librandi, <a href="/A220509/b220509.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = n^3 + 3*n + 3^n = A000578(n) + A008585(n) + A000244(n).

%F G.f.: (1 - 8*x^2 + 6*x^3 - 11*x^4)/((1-x)^4*(1-3*x)). - _Vincenzo Librandi_, Dec 18 2012

%e a(1) = 1^3 + 3*1 + 3^1 = 7.

%e a(2) = 2^3 + 3*2 + 3^2 = 23.

%t Table[n^3 + 3*n + 3^n, {n, 0, 30}] (* _T. D. Noe_, Dec 17 2012 *)

%t CoefficientList[Series[(1 - 8*x^2 + 6*x^3 - 11*x^4)/((1-x)^4*(1-3x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 18 2012 *)

%o (Maxima) A220509(n):=n^3+3*n+3^n$ makelist(A220509(n),n,0,20); /* _Martin Ettl_, Dec 17 2012 */

%o (Magma) [n^3 + 3*n + 3^n: n in [0..30]]; // _Vincenzo Librandi_, Dec 18 2012

%Y Cf. A000244, A000578, A008585, A220425, A220701.

%K nonn,easy

%O 0,2

%A _Jonathan Vos Post_, Dec 15 2012