A024039 a(n) = 4^n - n^3.

1, 3, 8, 37, 192, 899, 3880, 16041, 65024, 261415, 1047576, 4192973, 16775488, 67106667, 268432712, 1073738449, 4294963200, 17179864271, 68719470904, 274877900085, 1099511619776, 4398046501843, 17592186033768, 70368744165497, 281474976696832

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (8, -22, 28, -17, 4).

Programs

Magma

[4^n-n^3: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011

Mathematica

Table[4^n-n^3,{n,0,30}] (* or *) LinearRecurrence[{8,-22,28,-17,4},{1,3,8,37,192},31] (* Harvey P. Dale, Jul 26 2011 *)

Formula

G.f.: (-1 - 5*x^4 - 11*x^3 - 6*x^2 + 5*x)/((4*x-1)*(x-1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 13 2009

a(n) = 8*a(n-1) - 22*a(n-2) + 28*a(n-3) - 17*a(n-4) + 4*a(n-5); a(0)=1, a(1)=3, a(2)=8, a(3)=37, a(4)=192. - Harvey P. Dale, Jul 26 2011

Extensions

More terms from Harvey P. Dale, Jul 26 2011