A024019 2^n-n^9.

1, 1, -508, -19675, -262128, -1953093, -10077632, -40353479, -134217472, -387419977, -999998976, -2357945643, -5159776256, -10604491181, -20661030400, -38443326607, -68719411200, -118587745425, -198359028224, -322687173491, -511998951424, -794277949429

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..235

Index entries for linear recurrences with constant coefficients, signature (12,-65,210,-450,672,-714,540,-285,100,-21,2).

Formula

G.f.: (1 -11*x -455*x^2 -13724*x^3 -58808*x^4 +20026*x^5 + 224356*x^6 +161740*x^7 +28759*x^8 +993*x^9 +3*x^10) / ((1-2*x)*(1-x)^10). - Vincenzo Librandi, Oct 08 2014

a(n) = 12*a(n-1) -65*a(n-2) +210*a(n-3) -450*a(n-4) +672*a(n-5) -714*a(n-6) +540*a(n-7) -285*a(n-8) +100*a(n-9) -21*a(n-10) +2*a(n-11) for n>10. - Vincenzo Librandi, Oct 08 2014

Mathematica

Table[2^n - n^8, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 11 x - 455 x^2 - 13724 x^3 - 58808 x^4 + 20026 x^5 + 224356 x^6 + 161740 x^7 + 28759 x^8 + 993 x^9 + 3 x^10)/((1 - 2 x) (1 - x)^10), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 08 2014 *)

Prog

(Magma) [2^n-n^9: n in [0..30]]; // Vincenzo Librandi, Apr 30 2011
(Magma) I:=[1, 1, -508, -19675, -262128, -1953093, -10077632, -40353479, -134217472, -387419977, -999998976]; [n le 11 select I[n] else 12*Self(n -1)-65*Self(n-2)+210*Self(n-3)-450*Self(n-4)+672*Self(n-5)-714*Self(n -6)+540*Self(n-7)-285*Self(n-8)+100*Self(n-9)-21*Self(n-10)+2*Self(n -11): n in [1..35]]; // Vincenzo Librandi, Oct 08 2014

Crossrefs

Cf. sequences of the form k^n-n^9: this sequence (k=2), A024032 (k=3), A024045 (k=4), A024058 (k=5), A024071 (k=6), A024084 (k=7), A024097 (k=8), A024110 (k=9), A024123 (k=10), A024136 (k=11), A024149 (k=12).

Sequence in context: A028685 A152524 A236004 * A159686 A198195 A142819

Adjacent sequences: A024016 A024017 A024018 * A024020 A024021 A024022

Keyword

sign,easy

Author

N. J. A. Sloane.

Status

approved