A024053 a(n) = 5^n - n^4.

1, 4, 9, 44, 369, 2500, 14329, 75724, 386529, 1946564, 9755625, 48813484, 244119889, 1220674564, 6103477209, 30517527500, 152587825089, 762939369604, 3814697160649, 19073486197804, 95367431480625, 476837158008644, 2384185790781369, 11920928954798284

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (10,-35,60,-55,26,-5).

Formula

a(n) = 10*a(n-1) - 35*a(n-2) + 60*a(n-3) - 55*a(n-4) + 26*a(n-5) - 5*a(n-6).

From Elmo R. Oliveira, Apr 24 2026: (Start)

G.f.: (1 - 6*x + 4*x^2 + 34*x^3 + 59*x^4 + 4*x^5)/((1-5*x)*(1-x)^5).

E.g.f.: exp(5*x) - x*(1 + 7*x + 6*x^2 + x^3)*exp(x).

a(n) = A000351(n) - A000583(n). (End)

Mathematica

A024053[n_] := 5^n - n^4; Array[A024053, 25, 0] (* Paolo Xausa, May 05 2026 *)

Prog

(Magma) [5^n-n^4: n in [0..35]]; // Vincenzo Librandi, Jun 12 2011

Crossrefs

Cf. A000351, A000583.

Sequence in context: A209079 A149170 A357447 * A197970 A048892 A108849

Adjacent sequences: A024050 A024051 A024052 * A024054 A024055 A024056

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved