A024141 a(n) = 12^n - n.

1, 11, 142, 1725, 20732, 248827, 2985978, 35831801, 429981688, 5159780343, 61917364214, 743008370677, 8916100448244, 106993205379059, 1283918464548850, 15407021574586353, 184884258895036400, 2218611106740436975, 26623333280885243886, 319479999370622926829

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 (14,-25,12).

Crossrefs

Cf. numbers of the form k^n - n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), this sequence (k=12).

Programs

Magma

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

Magma

I:=[1, 11, 142]; [n le 3 select I[n] else 14*Self(n-1)-25*Self(n-2)+12*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013

Mathematica

Table[12^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 13 x^2) / ((1 - 12 x) (1 - x)^2),{x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
LinearRecurrence[{14,-25,12},{1,11,142},20] (* Harvey P. Dale, Nov 03 2024 *)

PARI

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

Formula

From Vincenzo Librandi, Jun 17 2013: (Start)

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

a(n) = 14*a(n-1) - 25*a(n-2) + 12*a(n-3). (End)

E.g.f.: exp(x)*(exp(11*x) - x). - Elmo R. Oliveira, Sep 10 2024