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%I #22 Sep 08 2022 08:44:48
%S 1,5,-28,-513,-2800,-7849,0,162287,1417472,9546255,59466176,361025495,
%T 2173796352,13055867207,78356634560,470173593951,2821093130240,
%U 16926635307167,101559922656192,609359692964615,3656158376062976,21936950554611735,131621703728887232,789730222905566927
%N a(n) = 6^n - n^6.
%C 6^n in the formula can be removed (for example) with the following Maple code: "with(gfun): rec1:={u1(0)=1,u1(n+1)=6*u1(n)}: rec2:={u2(n)=n^6}: poltorec(u1(n)-u2(n),[rec1,rec2],u1(n),u2(n)],a(n));". This yields a polynomial recurrence: {a(n+1)-5*n^6+6*n^5+15*n^4+20*n^3+15*n^2-6*a(n)+6*n+1, a(0) = 1} that can further be transformed into a linear recurrence with constant coefficients. - _Georg Fischer_, Feb 23 2021
%H Vincenzo Librandi, <a href="/A024068/b024068.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (13,-63,161,-245,231,-133,43,-6).
%F From _Chai Wah Wu_, Jan 26 2020: (Start)
%F a(n) = 13*a(n-1) - 63*a(n-2) + 161*a(n-3) - 245*a(n-4) + 231*a(n-5) - 133*a(n-6) + 43*a(n-7) - 6*a(n-8) for n > 7.
%F G.f.: (5*x^7 + 348*x^6 + 1734*x^5 + 1545*x^4 + 5*x^3 - 30*x^2 - 8*x + 1)/((x - 1)^7*(6*x - 1)). (End)
%t Table[6^n-n^6,{n,0,20}] (* _Harvey P. Dale_, Jan 30 2019 *)
%o (Magma) [6^n-n^6: n in [0..30]]; // _Vincenzo Librandi_, May 14 2011
%Y Cf. A024012, A024026, A058794, A024040, A024054. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Georg Fischer_, Feb 23 2021
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