A024093 a(n) = 8^n - n^5.

1, 7, 32, 269, 3072, 29643, 254368, 2080345, 16744448, 134158679, 1073641824, 8589773541, 68719227904, 549755442595, 4398045973280, 35184371329457, 281474975662080, 2251799812265391, 18014398507592416, 144115188073379773, 1152921504603646976

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (14,-63,140,-175,126,-49,8).

Formula

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

a(n) = 14*a(n-1) - 63*a(n-2) + 140*a(n-3) - 175*a(n-4) + 126*a(n-5) - 49*a(n-6) + 8*a(n-7) for n > 6.

G.f.: (-9*x^6 - 201*x^5 - 517*x^4 - 122*x^3 + 3*x^2 + 7*x - 1)/((x - 1)^6*(8*x - 1)). (End)

Mathematica

CoefficientList[Series[(-9*x^6 - 201*x^5 - 517*x^4 - 122*x^3 + 3*x^2 + 7*x - 1)/((x - 1)^6*(8*x - 1)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Nov 12 2022 *)
Table[8^n-n^5, {n, 0, 30}] (* or *) LinearRecurrence[{14, -63, 140, -175, 126, -49, 8}, {1, 7, 32, 269, 3072, 29643, 254368}, 30] (* Harvey P. Dale, Nov 26 2025 *)

Prog

(Magma) [8^n-n^5: n in [0..20]]; // Vincenzo Librandi, Jul 05 2011
(PARI) a(n)=8^n-n^5 \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Sequence in context: A188331 A177766 A240390 * A110323 A288721 A324412

Adjacent sequences: A024090 A024091 A024092 * A024094 A024095 A024096

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved