A024015 - OEIS

%I #22 Sep 08 2022 08:44:48

%S 1,1,-28,-235,-1008,-3093,-7712,-16679,-32512,-58537,-98976,-159003,

%T -244736,-363101,-521440,-726607,-983040,-1288785,-1627424,-1951811,

%U -2151424,-1986949,-959328,1952265,8814592,23788807,55227488,119868821,251225088

%N 2^n-n^5.

%H Vincenzo Librandi, <a href="/A024015/b024015.txt">Table of n, a(n) for n = 0..230</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-27,50,-55,36,-13,2).

%F G:f.: (1-7*x-9*x^2-34*x^3+121*x^4+45*x^5+3*x^6) / ((1-2*x)*(1-x)^6). - _Vincenzo Librandi_, Oct 07 2014

%F a(n) = 8*a(n-1) -27*a(n-2) +50*a(n-3) -55*a(n-4) +36*a(n-5) -13*a(n-6) +2*a(n-7) for n>6. - _Vincenzo Librandi_, Oct 07 2014

%t Table[2^n - n^5, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 7 x - 9 x^2 - 34 x^3 + 121 x^4 + 45 x^5 + 3 x^6)/((1 - 2 x) (1 - x)^6), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 07 2014 *)

%t LinearRecurrence[{8,-27,50,-55,36,-13,2},{1,1,-28,-235,-1008,-3093,-7712},30] (* _Harvey P. Dale_, May 14 2016 *)

%o (Magma) [2^n-n^5: n in [0..35]]; // _Vincenzo Librandi_, Apr 29 2011

%o (Magma) I:=[1,1,-28,-235,-1008,-3093,-7712]; [n le 7 select I[n] else 8*Self(n-1)-27*Self(n-2)+50*Self(n-3)-55*Self(n-4)+36*Self(n-5)-13*Self(n-6)+2*Self(n-7): n in [1..35]]; // _Vincenzo Librandi_, Oct 07 2014

%Y Cf. sequences of the form k^n-n^5: this sequence (k=2), A024028 (k=3), A024041 (k=4), A024054 (k=5), A024067 (k=6), A024080 (k=7), A024093 (k=8), A024106 (k=9), A024119 (k=10), A024132 (k=11), A024145 (k=12).

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_.