A024055 a(n) = 5^n - n^6.

1, 4, -39, -604, -3471, -12500, -31031, -39524, 128481, 1421684, 8765625, 47056564, 241154641, 1215876316, 6095986089, 30506187500, 152571113409, 762915315556, 3814663253401, 19073439282244, 95367367640625

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (12, -56, 140, -210, 196, -112, 36, -5).

Programs

Magma

[5^n-n^6: n in [0..30]]; // Vincenzo Librandi, Jul 03 2011

Mathematica

Table[5^n-n^6,{n,0,60}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
LinearRecurrence[{12,-56,140,-210,196,-112,36,-5},{1,4,-39,-604,-3471,-12500,-31031,-39524},61] (* Harvey P. Dale, Jul 21 2011 *)

Formula

a(n) = 12*a(n-1) - 56*a(n-2) + 140*a(n-3) - 210*a(n-4) + 196*a(n-5) - 112*a(n-6) + 36*a(n-7) - 5*a(n-8), a(0)=1, a(1)=4, a(2)=-39, a(3)=-604, a(4)=-3471, a(5)=-12500, a(6)=-31031, a(7)=-39524. - Harvey P. Dale, Jul 21 2011

G.f.: (1 - 8*x - 31*x^2 - 52*x^3 + 1243*x^4 + 1432*x^5 + 291*x^6 + 4*x^7)/((1-5*x)*(1-x)^7). - Bruno Berselli, Jul 21 2011