A024051 a(n) = 5^n - n^2.

1, 4, 21, 116, 609, 3100, 15589, 78076, 390561, 1953044, 9765525, 48828004, 244140481, 1220702956, 6103515429, 30517577900, 152587890369, 762939452836, 3814697265301, 19073486327764, 95367431640225, 476837158202684, 2384185791015141, 11920928955077596

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-18,16,-5).

Formula

a(n) = 8*a(n-1) - 18*a(n-2) + 16*a(n-3) - 5*a(n-4).

From Elmo R. Oliveira, Nov 13 2025: (Start)

G.f.: (1 - 4*x + 7*x^2 + 4*x^3)/((1-x)^3*(1-5*x)).

E.g.f.: exp(5*x) - x*(1 + x)*exp(x).

a(n) = A000351(n) - A000290(n). (End)

Mathematica

Table[5^n-n^2, {n, 0, 20}] (* or *) LinearRecurrence[{8, -18, 16, -5}, {1, 4, 21, 116}, 30] (* Harvey P. Dale, Nov 22 2012 *)

Prog

(Magma) [5^n-n^2: n in [0..35]]; // Vincenzo Librandi, Jun 12 2011

Crossrefs

Cf. A000290, A000351.

Sequence in context: A240436 A255139 A015554 * A180908 A212419 A020048

Adjacent sequences: A024048 A024049 A024050 * A024052 A024053 A024054

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved