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

1, 7, -192, -6049, -61440, -357857, -1417472, -3667649, 0, 91171007, 973741824, 8375575711, 68289495040, 548940083167, 4396570722048, 35181809198207, 281470681743360, 2251792837927807, 18014387489521408, 144115171092292831

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (17, -108, 372, -798, 1134, -1092, 708, -297, 73, -8).

Formula

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

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

Mathematica

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 *)

Prog

(Magma) [8^n-n^8: n in [0..25]]; // Vincenzo Librandi, May 16 2011
(PARI) a(n)=8^n-n^8 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A024012, A024026, A058794, A024040, A024054, A024068, A024082. - Vladimir Joseph Stephan Orlovsky, Jan 15 2009

Sequence in context: A200819 A232146 A264353 * A030257 A159826 A012849

Adjacent sequences: A024093 A024094 A024095 * A024097 A024098 A024099

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved