A024067 a(n) = 6^n - n^5.

1, 5, 4, -27, 272, 4651, 38880, 263129, 1646848, 10018647, 60366176, 362636005, 2176533504, 13060322723, 78363626272, 470184225201, 2821108858880, 16926658024879, 101559954778848, 609359737534397, 3656158436862976, 21936950636293755, 131621703837113504

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (12,-51,110,-135,96,-37,6).

Formula

a(n) = 12*a(n-1) - 51*a(n-2) + 110*a(n-3) - 135*a(n-4) + 96*a(n-5) - 37*a(n-6) + 6*a(n-7); a(0)=1, a(1)=5, a(2)=4, a(3)=-27, a(4)=272, a(5)=4651, a(6)=38880. - Harvey P. Dale, Apr 08 2015

From Elmo R. Oliveira, Jun 01 2026: (Start)

G.f.: (1 - 7*x - 5*x^2 + 70*x^3 + 385*x^4 + 149*x^5 + 7*x^6)/((1-6*x)*(x-1)^6).

E.g.f.: exp(6*x) - x*exp(x)*(1 + 15*x + 25*x^2 + 10*x^3 + x^4).

a(n) = A000400(n) - A000584(n). (End)

Mathematica

Table[6^n-n^5, {n, 0, 20}] (* Harvey P. Dale, Apr 08 2015 *)
(* Alternative: *)
LinearRecurrence[{12, -51, 110, -135, 96, -37, 6}, {1, 5, 4, -27, 272, 4651, 38880}, 20] (* Harvey P. Dale, Apr 08 2015 *)

Prog

(Magma) [6^n-n^5: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011

Crossrefs

Cf. A000400, A000584.

Sequence in context: A248255 A277058 A275960 * A361983 A192778 A051138

Adjacent sequences: A024064 A024065 A024066 * A024068 A024069 A024070

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved