A024105 a(n) = 9^n - n^4.

1, 8, 65, 648, 6305, 58424, 530145, 4780568, 43042625, 387413928, 3486774401, 31381044968, 282429515745, 2541865799768, 22876792416545, 205891132044024, 1853020188786305, 16677181699583048, 150094635296894145

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (14,-55,100,-95,46,-9).

Crossrefs

Cf. A000583, A001019.

Programs

Magma

[9^n-n^4: n in [0..25]]; // Vincenzo Librandi, Jul 06 2011

Mathematica

Table[9^n-n^4,{n,0,25}] (* or *) LinearRecurrence[{14,-55,100,-95,46,-9},{1,8,65,648,6305,58424},30] (* Harvey P. Dale, Oct 07 2013 *)

Formula

a(n) = 14*a(n-1) - 55*a(n-2) + 100*a(n-3) - 95*a(n-4) + 46*a(n-5) - 9*a(n-6); a(0)=1, a(1)=8, a(2)=65, a(3)=648, a(4)=6305, a(5)=58424. - Harvey P. Dale, Oct 07 2013

G.f.: (1 - 6*x + 8*x^2 + 78*x^3 + 103*x^4 + 8*x^5)/((1 - x)^5*(1 - 9*x)). - Stefano Spezia, Aug 01 2022