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.
%I A024013 #22 Jul 08 2025 17:25:45 %S A024013 1,1,-4,-19,-48,-93,-152,-215,-256,-217,24,717,2368,5995,13640,29393, %T A024013 61440,126159,256312,517429,1040576,2087891,4183656,8376441,16763392, %U A024013 33538807,67091288,134198045,268413504,536846523,1073714824,2147453857,4294934528 %N A024013 2^n-n^3. %H A024013 Vincenzo Librandi, <a href="/A024013/b024013.txt">Table of n, a(n) for n = 0..240</a> %H A024013 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2). %F A024013 G.f.: (-1-3*x^4-3*x^3-4*x^2+5*x)/((-1+2*x)*(x-1)^4). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009] %F A024013 a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-9*a(n-4)+2*a(n-5) for n>4. - _Vincenzo Librandi_, Oct 06 2014 %p A024013 A024013:=n->2^n-n^3: seq(A024013(n), n=0..40); # _Wesley Ivan Hurt_, Oct 21 2014 %t A024013 Table[2^n-n^3,{n,0,80}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *) %o A024013 (Magma) [2^n-n^3: n in [0..35]]; // _Vincenzo Librandi_, Apr 29 2011 %o A024013 (Magma) I:=[1,1,-4,-19,-48]; [n le 5 select I[n] else 6*Self(n-1)-14*Self(n-2)+16*Self(n-3)-9*Self(n-4)+2*Self(n-5): n in [1..35]]; // _Vincenzo Librandi_, Oct 06 2014 %Y A024013 Cf. sequences of the form k^n-n^3: this sequence (k=2), A024026 (k=3), A024039 (k=4), A024052 (k=5), A024065 (k=6), A024078 (k=7), A024091 (k=8), A024104 (k=9), A024117 (k=10), A024130 (k=11), A024143 (k=12). %K A024013 sign,easy %O A024013 0,3 %A A024013 _N. J. A. Sloane_