cp's OEIS Frontend

A024089 a(n) = 8^n - n.

%I A024089 #21 Sep 10 2024 14:52:54
%S A024089 1,7,62,509,4092,32763,262138,2097145,16777208,134217719,1073741814,
%T A024089 8589934581,68719476724,549755813875,4398046511090,35184372088817,
%U A024089 281474976710640,2251799813685231,18014398509481966,144115188075855853,1152921504606846956,9223372036854775787
%N A024089 a(n) = 8^n - n.
%H A024089 Vincenzo Librandi, <a href="/A024089/b024089.txt">Table of n, a(n) for n = 0..400</a>
%H A024089 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17,8).
%F A024089 From _Vincenzo Librandi_, Jun 17 2013: (Start)
%F A024089 G.f.: (1-3*x+9*x^2)/((1-8*x)*(1-x)^2).
%F A024089 a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3). (End)
%F A024089 E.g.f.: exp(x)*(exp(7*x) - x). - _Elmo R. Oliveira_, Sep 10 2024
%t A024089 Table[8^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 9 x^2) / ((1 - 8 x) (1 - x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 17 2013 *)
%t A024089 LinearRecurrence[{10,-17,8},{1,7,62},30] (* _Harvey P. Dale_, Sep 28 2017 *)
%o A024089 (Magma) [8^n-n: n in [0..20]]; // _Vincenzo Librandi_, Jul 05 2011
%o A024089 (Magma) I:=[1,7,62]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 17 2013
%o A024089 (PARI) a(n)=8^n-n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A024089 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), this sequence (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).
%Y A024089 Cf. A198855 (first differences).
%K A024089 nonn,easy
%O A024089 0,2
%A A024089 _N. J. A. Sloane_