%I #21 Feb 09 2022 19:40:54

%S 0,3,6,9,39,69,99,399,699,999,3999,6999,9999,39999,69999,99999,399999,

%T 699999,999999,3999999,6999999,9999999,39999999,69999999,99999999,

%U 399999999,699999999,999999999,3999999999,6999999999,9999999999,39999999999,69999999999

%N Smallest number whose sum of digits is 3n.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,10,-10).

%F a(n) = 1/3 * A133201(n).

%F a(n) = a(n-1)+10*a(n-3)-10*a(n-4). G.f.: 3*x*(x^2+x+1) / ((x-1)*(10*x^3-1)). [_Colin Barker_, Feb 01 2013]

%t LinearRecurrence[{1,0,10,-10},{0,3,6,9},40] (* _Harvey P. Dale_, Oct 01 2018 *)

%o (Python)

%o def a(n): q, r = divmod(3*n, 9); return int(str(r) + "9"*q)

%o print([a(n) for n in range(31)]) # _Michael S. Branicky_, Feb 07 2022

%Y Cf. A133201.

%K nonn,base,easy

%O 0,2

%A _Paul Curtz_, Oct 09 2007