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a(n) = 8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.
6

%I #20 Apr 11 2024 03:53:31

%S -6,-20,-76,-272,-580,3760,77324,896848,8869820,81550960,719926124,

%T 6196609168,52439953820,438516694960,3635082523724,29935019892688,

%U 245264010263420,2001462391659760,16280541150478124,132087583623451408

%N a(n) = 8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.

%H Harvey P. Dale, <a href="/A147979/b147979.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).

%F G.f.: 2*x*(49752*x^7-105056*x^6+87794*x^5-38129*x^4+9380*x^3-1316*x^2+98*x-3)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)). - _Colin Barker_, Oct 29 2012

%t lst={};Do[p=8^n-7^n-6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst

%t Table[8^n-Total[Range[7]^n],{n,0,20}] (* or *) LinearRecurrence[{36,-546,4536,-22449,67284,-118124,109584,-40320},{-6,-20,-76,-272,-580,3760,77324,896848},20] (* _Harvey P. Dale_, Nov 15 2014 *)

%o (PARI) a(n)=8^n-7^n-6^n-5^n-4^n-3^n-2^n-1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A147975, A147976, A147977, A147978.

%K sign,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Nov 18 2008