A024028 a(n) = 3^n - n^5.

1, 2, -23, -216, -943, -2882, -7047, -14620, -26207, -39366, -40951, 16096, 282609, 1223030, 4245145, 13589532, 41998145, 127720306, 385530921, 1159785368, 3483584401

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (9,-33,65,-75,51,-19,3).

Crossrefs

Cf. A000244 (3^n), A000584 (n^5).

Programs

Magma

[3^n-n^5 : n in [0..30]]; // Vincenzo Librandi, May 17 2011

Mathematica

Table[3^n-n^5,{n,0,30}] (* or  *) LinearRecurrence[{9,-33,65,-75,51,-19,3},{1,2,-23,-216,-943,-2882,-7047},30] (* Harvey P. Dale, Dec 16 2021 *)

Formula

a(n) = 3^n - n^5.

From Chai Wah Wu, Jul 10 2016: (Start)

a(n) = 9*a(n-1) - 33*a(n-2) + 65*a(n-3) - 75*a(n-4) + 51*a(n-5) - 19*a(n-6) + 3*a(n-7) for n > 6.

G.f.: (-4*x^6 - 71*x^5 - 187*x^4 + 8*x^3 + 8*x^2 + 7*x - 1)/((x - 1)^6*(3*x - 1)). (End)