A004142 a(n) = n*(3^n - 2^n).

0, 1, 10, 57, 260, 1055, 3990, 14413, 50440, 172539, 580250, 1926089, 6328140, 20619703, 66732190, 214742085, 687698960, 2193154547, 6968850210, 22073006401, 69714716500, 219623377071, 690291036710

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (10,-37,60,-36).

Formula

From R. J. Mathar, Feb 10 2022: (Start)

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

a(n) = A036290(n) - A036289(n). (End)

Mathematica

Table[n(3^n-2^n), {n, 0, 30}] (* Harvey P. Dale, Sep 04 2023 *)
(* Alternative: *)
LinearRecurrence[{10, -37, 60, -36}, {0, 1, 10, 57}, 30] (* Harvey P. Dale, Sep 04 2023 *)

Crossrefs

Equals n * A001047(n).

Sequence in context: A055251 A038733 A392583 * A006529 A337001 A246754

Adjacent sequences: A004139 A004140 A004141 * A004143 A004144 A004145

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved