A024142 a(n) = 12^n - n^2.

1, 11, 140, 1719, 20720, 248807, 2985948, 35831759, 429981632, 5159780271, 61917364124, 743008370567, 8916100448112, 106993205378903, 1283918464548668, 15407021574586143, 184884258895036160, 2218611106740436703, 26623333280885243580, 319479999370622926487

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (15,-39,37,-12).

Formula

G.f.: (1-4*x+14*x^2+11*x^3)/((1-12*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014

From Elmo R. Oliveira, Jul 10 2026: (Start)

E.g.f.: exp(12*x) - x*(1 + x)*exp(x).

a(n) = A001021(n) - A000290(n).

a(n) = 15*a(n-1) - 39*a(n-2) + 37*a(n-3) - 12*a(n-4). (End)

Mathematica

Table[12^n - n^2, {n, 0, 25}] (* Vincenzo Librandi, Oct 06 2014 *)
(* Alternative: *)
CoefficientList[Series[(1 - 4 x + 14 x^2 + 11 x^3)/((1 - 12 x) (1 - x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)

Prog

(Magma) [12^n-n^2: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
(PARI) a(n)=12^n-n^2 \\ Charles R Greathouse IV, Jul 01 2011

Crossrefs

Cf. similar sequences listed in A024025.

Cf. A000290, A001021.

Sequence in context: A003378 A385056 A142930 * A024296 A324084 A141907

Adjacent sequences: A024139 A024140 A024141 * A024143 A024144 A024145

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved