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A024096 a(n) = 8^n - n^8. 7

%I #25 Sep 08 2022 08:44:48

%S 1,7,-192,-6049,-61440,-357857,-1417472,-3667649,0,91171007,973741824,

%T 8375575711,68289495040,548940083167,4396570722048,35181809198207,

%U 281470681743360,2251792837927807,18014387489521408,144115171092292831

%N a(n) = 8^n - n^8.

%H Vincenzo Librandi, <a href="/A024096/b024096.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (17, -108, 372, -798, 1134, -1092, 708, -297, 73, -8).

%F G.f.: (1 - 10*x - 203*x^2 - 2401*x^3 + 18851*x^4 + 109207*x^5 + 120743*x^6 + 34061*x^7 + 1984*x^8 + 7*x^9) / ((1-8*x)*(1-x)^9). - _Bruno Berselli_, May 16 2011

%F a(0)=1, a(1)=7, a(2)=-192, a(3)=-6049, a(4)=-61440, a(5)=-357857, a(6)=-1417472, a(7)=-3667649, a(8)=0, a(9)=91171007; for n>9, a(n) = 17*a(n-1) - 108*a(n-2) + 372*a(n-3) - 798*a(n-4) + 1134*a(n-5) - 1092*a(n-6) + 708*a(n-7) - 297*a(n-8) + 73*a(n-9) - 8*a(n-10). - _Harvey P. Dale_, Oct 10 2013

%t Table[8^n - n^8, {n, 0, 20}] (* or *) LinearRecurrence[ {17, -108, 372, -798, 1134, -1092, 708, -297, 73, -8}, {1, 7, -192, -6049, -61440, -357857, -1417472, -3667649, 0, 91171007}, 20] (* _Harvey P. Dale_, Oct 10 2013 *)

%o (Magma) [8^n-n^8: n in [0..25]]; // _Vincenzo Librandi_, May 16 2011

%o (PARI) a(n)=8^n-n^8 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A024012, A024026, A058794, A024040, A024054, A024068, A024082. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)