A024013 2^n-n^3.

1, 1, -4, -19, -48, -93, -152, -215, -256, -217, 24, 717, 2368, 5995, 13640, 29393, 61440, 126159, 256312, 517429, 1040576, 2087891, 4183656, 8376441, 16763392, 33538807, 67091288, 134198045, 268413504, 536846523, 1073714824, 2147453857, 4294934528

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..240
• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Crossrefs

Cf. sequences of the form k^n-n^3: this sequence (k=2), A024026 (k=3), A024039 (k=4), A024052 (k=5), A024065 (k=6), A024078 (k=7), A024091 (k=8), A024104 (k=9), A024117 (k=10), A024130 (k=11), A024143 (k=12).

Programs

Magma

[2^n-n^3: n in [0..35]]; // Vincenzo Librandi, Apr 29 2011

Magma

I:=[1,1,-4,-19,-48]; [n le 5 select I[n] else 6*Self(n-1)-14*Self(n-2)+16*Self(n-3)-9*Self(n-4)+2*Self(n-5): n in [1..35]]; // Vincenzo Librandi, Oct 06 2014

Maple

A024013:=n->2^n-n^3: seq(A024013(n), n=0..40); # Wesley Ivan Hurt, Oct 21 2014

Mathematica

Table[2^n-n^3,{n,0,80}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

Formula

G.f.: (-1-3*x^4-3*x^3-4*x^2+5*x)/((-1+2*x)*(x-1)^4). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009]

a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-9*a(n-4)+2*a(n-5) for n>4. - Vincenzo Librandi, Oct 06 2014