A024143 a(n) = 12^n - n^3.

1, 11, 136, 1701, 20672, 248707, 2985768, 35831465, 429981184, 5159779623, 61917363224, 743008369357, 8916100446528, 106993205376875, 1283918464546120, 15407021574582993, 184884258895032320, 2218611106740432079, 26623333280885238072, 319479999370622919989

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (16,-54,76,-49,12).

Programs

Magma

[12^n-n^3: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011

Mathematica

LinearRecurrence[{16,-54,76,-49,12},{1,11,136,1701,20672},20] (* Harvey P. Dale, Jun 15 2025 *)

PARI

a(n)=12^n-n^3 \\ Charles R Greathouse IV, Jul 01 2011

PARI

Vec((1 - 5*x + 14*x^2 + 43*x^3 + 13*x^4) / ((1 - x)^4*(1 - 12*x)) + O(x^20)) \\ Colin Barker, Oct 11 2018

Formula

From Colin Barker, Oct 11 2018: (Start)

G.f.: (1 - 5*x + 14*x^2 + 43*x^3 + 13*x^4) / ((1 - x)^4*(1 - 12*x)).

a(n) = 16*a(n-1) - 54*a(n-2) + 76*a(n-3) - 49*a(n-4) + 12*a(n-5) for n>4.

(End)