A024016 - OEIS

%I #21 Jan 29 2026 20:11:05

%S 1,1,-60,-721,-4080,-15593,-46592,-117521,-261888,-530929,-998976,

%T -1769513,-2981888,-4818617,-7513152,-11357857,-16711680,-24006497,

%U -33750080,-46521593,-62951424,-83668969,-109185600,-139647281,-174325760,-210586193,-241806912

%N a(n) = 2^n-n^6.

%H Vincenzo Librandi, <a href="/A024016/b024016.txt">Table of n, a(n) for n = 0..239</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (9,-35,77,-105,91,-49,15,-2).

%F G.f.: (1-8*x-34*x^2-223*x^3+337*x^4+526*x^5+120*x^6+x^7) / ((1-2* x)*(1-x)^7). - _Vincenzo Librandi_, Oct 07 2014

%F a(n) = 9*a(n-1) -35*a(n-2) +77*a(n-3) -105*a(n-4) +91*a(n-5) -49*a(n-6) +15*a(n-7) -2*a(n-8) for n>7. - _Vincenzo Librandi_, Oct 07 2014

%t Table[2^n - n^6, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 8 x - 34 x^2 - 223 x^3 + 337 x^4 + 526 x^5 + 120 x^6 + x^7)/((1 - 2 x) (1 - x)^7), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 07 2014 *)

%t LinearRecurrence[{9,-35,77,-105,91,-49,15,-2},{1,1,-60,-721,-4080,-15593,-46592,-117521},30] (* _Harvey P. Dale_, Oct 04 2019 *)

%o (Magma) [2^n-n^6: n in [0..25]]; // _Vincenzo Librandi_, Apr 30 2011

%o (Magma) I:=[1,1,-60,-721,-4080,-15593,-46592,-117521]; [n le 8 select I[n] else 9*Self(n-1)-35*Self(n-2)+77*Self(n-3)-105*Self(n-4)+91*Self(n-5)-49*Self(n-6)+15*Self(n-7)-2*Self(n-8): n in [1..35]]; // _Vincenzo Librandi_, Oct 07 2014

%Y Cf. sequences of the form k^n-n^6: this sequence (k=2), A024029 (k=3), A024042 (k=4), A024055 (k=5), A024068 (k=6), A024081 (k=7), A024094 (k=8), A024107 (k=9), A024120 (k=10), A024133 (k=11), A024146 (k=12).

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_