%I #24 Nov 03 2024 10:45:05

%S 1,11,142,1725,20732,248827,2985978,35831801,429981688,5159780343,

%T 61917364214,743008370677,8916100448244,106993205379059,

%U 1283918464548850,15407021574586353,184884258895036400,2218611106740436975,26623333280885243886,319479999370622926829

%N a(n) = 12^n - n.

%H Vincenzo Librandi, <a href="/A024141/b024141.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-25,12).

%F From _Vincenzo Librandi_, Jun 17 2013: (Start)

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

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

%F E.g.f.: exp(x)*(exp(11*x) - x). - _Elmo R. Oliveira_, Sep 10 2024

%t 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 *)

%t LinearRecurrence[{14,-25,12},{1,11,142},20] (* _Harvey P. Dale_, Nov 03 2024 *)

%o (Magma) [12^n-n: n in [0..20]]; // _Vincenzo Librandi_, Jul 01 2011

%o (PARI) a(n)=12^n-n \\ _Charles R Greathouse IV_, Jul 01 2011

%o (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

%Y 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).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_