A001585 a(n) = 3^n + n^3.

1, 4, 17, 54, 145, 368, 945, 2530, 7073, 20412, 60049, 178478, 533169, 1596520, 4785713, 14352282, 43050817, 129145076, 387426321, 1162268326, 3486792401, 10460362464, 31381070257, 94143190994, 282429550305, 847288625068

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

In this sequence if we do a forward difference, then the 4th forward difference when considered as a sequence will be a geometric progression with common ratio 3. - Gopalakrishnan (gopala498(AT)yahoo.co.in), May 26 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• R. K. Hoeflin, Titan Test
• Index entries for linear recurrences with constant coefficients, signature (7, -18, 22, -13, 3).

Crossrefs

Cf. A001580.

Programs

Magma

[3^n+n^3: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011

Maple

seq(seq(k^n+n^k, k=3..3), n=0..23); # Zerinvary Lajos, Jun 29 2007

Mathematica

Table[3^n+n^3,{n,0,3*4!}] (* Vladimir Joseph Stephan Orlovsky, May 07 2010 *)

Formula

G.f.: (-1+2*x^4+15*x^3-7*x^2+3*x)/((3*x-1)*(x-1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, May 07 2010