A083316 a(n) = (2*6^n - (5^n - 3^n))/2.

1, 5, 28, 167, 1024, 6335, 39208, 241967, 1487584, 9110975, 55612888, 338471567, 2054977744, 12451139615, 75314797768, 454933369967, 2744837485504, 16545254288255, 99652801745848, 599823577977167, 3608476467634864, 21698537291452895, 130429626637289128, 783769805647653167

Offset: 0

Author

Paul Barry, Apr 24 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083315.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-63,90).

Crossrefs

Cf. A083315.

Programs

Mathematica

A083316[n_] := 6^n - (5^n - 3^n)/2; Array[A083316, 25, 0] (* or *)
LinearRecurrence[{14, -63, 90}, {1, 5, 28}, 25] (* Paolo Xausa, Jun 27 2025 *)

Formula

G.f.: (1-9x+21x^2)/((1-3x)(1-5x)(1-6x)).

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

a(n) = 14*a(n-1) - 63*a(n-2) + 90*a(n-3). - Wesley Ivan Hurt, Jun 26 2025