A246767 a(n) = n^4 - 2n.

0, -1, 12, 75, 248, 615, 1284, 2387, 4080, 6543, 9980, 14619, 20712, 28535, 38388, 50595, 65504, 83487, 104940, 130283, 159960, 194439, 234212, 279795, 331728, 390575, 456924, 531387, 614600, 707223, 809940, 923459, 1048512, 1185855, 1336268, 1500555, 1679544, 1874087, 2085060

Offset: 1

Author

Derek Orr, Sep 04 2014

Keywords

• sign
• easy

Comments

For n > 0, a(n) is the largest number k such that k + n divides k + n^4, or -1 if k is infinite. In general, for m > 0 and n > 0, the largest number k such that k + n divides k + n^m is given by k = n^m - 2*n. If k = -1 (when n = 1 for any m or when m = 1 for any n), it is infinite.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A067998, A242135, A242436.

Programs

Mathematica

Table[n^4-2n,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,-1,12,75,248},40] (* Harvey P. Dale, May 05 2019 *)

PARI

vector(100,n,(n-1)^4-2*(n-1))

PARI

concat(0, Vec(-x^2*(3*x^3+5*x^2+17*x-1)/(x-1)^5 + O(x^100))) \\ Colin Barker, Sep 04 2014

Formula

G.f.: -x^2*(3*x^3+5*x^2+17*x-1) / (x-1)^5. - Colin Barker, Sep 04 2014

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Jun 07 2021