cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A024076 a(n) = 7^n - n.

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%I A024076 #24 Sep 10 2024 14:42:06
%S A024076 1,6,47,340,2397,16802,117643,823536,5764793,40353598,282475239,
%T A024076 1977326732,13841287189,96889010394,678223072835,4747561509928,
%U A024076 33232930569585,232630513987190,1628413597910431,11398895185373124,79792266297611981,558545864083283986,3909821048582988027
%N A024076 a(n) = 7^n - n.
%H A024076 Vincenzo Librandi, <a href="/A024076/b024076.txt">Table of n, a(n) for n = 0..500</a>
%H A024076 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-15,7).
%F A024076 From _Vincenzo Librandi_, Jun 16 2013: (Start)
%F A024076 G.f.: (1-3*x+8*x^2)/((1-7*x)*(1-x)^2).
%F A024076 a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). (End)
%F A024076 E.g.f.: exp(x)*(exp(6*x) - x). - _Elmo R. Oliveira_, Sep 10 2024
%p A024076 A024076:=n->7^n-n; seq(A024076(n), n=0..30); # _Wesley Ivan Hurt_, Jan 24 2014
%t A024076 Table[7^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 8 x^2) / ((1 - 7 x) (1 - x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 16 2013 *)
%o A024076 (Magma) [7^n-n: n in [0..25]]; // _Vincenzo Librandi_, Jul 03 2011
%o A024076 (Magma) I:=[1, 6, 47]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 16 2013
%o A024076 (PARI) a(n)=7^n-n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A024076 Cf. numbers of the form k^n - n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), this sequence (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).
%Y A024076 Cf. A198688 (first differences).
%K A024076 nonn,easy
%O A024076 0,2
%A A024076 _N. J. A. Sloane_