A024017 a(n) = 2^n - n^7.

1, 1, -124, -2179, -16368, -78093, -279872, -823415, -2096896, -4782457, -9998976, -19485123, -35827712, -62740325, -105397120, -170826607, -268369920, -410207601, -611957888, -893347451, -1278951424, -1798991389, -2490163584, -3396436839

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..239

Index entries for linear recurrences with constant coefficients, signature (10,-44,112,-182,196,-140,64,-17,2).

Formula

G.f.: (1-9*x-90*x^2-1007*x^3+36*x^4+3585*x^5+ 2290*x^6 +231*x^7+3*x^8)/((1-2*x)*(1-x)^8). - Vincenzo Librandi, Oct 07 2014

a(n) = 10*a(n-1)-44*a(n-2)+112*a(n-3)-182*a(n-4)+196*a(n-5)-140*a(n-6)+64*a(n-7)-17*a(n-8)+2*a(n-9). - Vincenzo Librandi, Oct 07 2014

Mathematica

Table[2^n - n^7, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 9 x - 90 x^2 - 1007 x^3 + 36 x^4 + 3585 x^5 + 2290 x^6 + 231 x^7 + 3 x^8)/((1 - 2 x) (1 - x)^8), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 07 2014 *)
LinearRecurrence[{10, -44, 112, -182, 196, -140, 64, -17, 2}, {1, 1, -124, -2179, -16368, -78093, -279872, -823415, -2096896}, 30] (* Harvey P. Dale, Feb 28 2023 *)

Prog

(Magma) [2^n-n^7: n in [0..25]]; // Vincenzo Librandi, Apr 30 2011
(Magma) I:=[1, 1, -124, -2179, -16368, -78093, -279872, -823415, -2096896]; [n le 9 select I[n] else 10*Self(n-1)-44*Self(n-2)+112*Self(n-3)-182*Self(n-4)+196*Self(n-5)-140*Self(n-6)+64*Self(n-7)-17*Self(n-8)+2*Self(n-9): n in [1..35]]; // Vincenzo Librandi, Oct 07 2014

Crossrefs

Cf. sequences of the form k^n-n^7: this sequence (k=2), A024030 (k=3), A024043 (k=4), A024056 (k=5), A024069 (k=6), A024082 (k=7), A024095 (k=8), A024108 (k=9), A024121 (k=10), A024134 (k=11), A024147 (k=12).

Sequence in context: A185860 A204634 A327339 * A260097 A232796 A263544

Adjacent sequences: A024014 A024015 A024016 * A024018 A024019 A024020

Keyword

sign,easy

Author

N. J. A. Sloane.

Status

approved