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, 2541865845905, 7625597504670, 22876792476913

Offset

0,2

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

Ronald K. Hoeflin, The Titan Test.

Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).

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

From Elmo R. Oliveira, Dec 25 2025: (Start)

E.g.f.: exp(x)*(x*(1 + 3*x + x^2) + exp(2*x)).

a(n) = 7*a(n-1) - 18*a(n-2) + 22*a(n-3) - 13*a(n-4) + 3*a(n-5). (End)

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 *)

Prog

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

Crossrefs

Cf. A001580.

Sequence in context: A208658 A092091 A046995 * A060262 A157492 A108140

Adjacent sequences: A001582 A001583 A001584 * A001586 A001587 A001588

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, May 07 2010

Status

approved