login
a(n) = n*(3^n - 2^n).
0

%I #12 Oct 24 2023 20:29:23

%S 0,1,10,57,260,1055,3990,14413,50440,172539,580250,1926089,6328140,

%T 20619703,66732190,214742085,687698960,2193154547,6968850210,

%U 22073006401,69714716500,219623377071,690291036710

%N a(n) = n*(3^n - 2^n).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-37,60,-36).

%F From _R. J. Mathar_, Feb 10 2022: (Start)

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

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

%t Table[n(3^n-2^n),{n,0,30}] (* or *) LinearRecurrence[{10,-37,60,-36},{0,1,10,57},30] (* _Harvey P. Dale_, Sep 04 2023 *)

%Y Equals n * A001047(n).

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_