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%I #19 Sep 08 2022 08:44:48
%S 1,11,142,1725,20732,248827,2985978,35831801,429981688,5159780343,
%T 61917364214,743008370677,8916100448244,106993205379059,
%U 1283918464548850,15407021574586353,184884258895036400
%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 G.f.: (1 - 3*x + 13*x^2)/((1-12*x)*(1-x)^2). - _Vincenzo Librandi_, Jun 17 2013
%F a(n) = 14*a(n-1) - 25*a(n-2) + 12*a(n-3). - _Vincenzo Librandi_, Jun 17 2013
%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 *)
%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_
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