%I #10 Mar 05 2023 13:17:38

%S 1,14,144,1444,14444,144444,1444444,14444444,144444444,1444444444,

%T 14444444444,144444444444,1444444444444,14444444444444,

%U 144444444444444,1444444444444444,14444444444444444,144444444444444444

%N Expansion of (1+3x)/((1-x)(1-10x)).

%C Partial sums of (1+3x)/(1-10x)={1,13,130,1300,...}.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n)=10^n*13/9-4/9; a(n)=11a(n-1)-10a(n-2), a(0)=1, a(1)=14.

%t CoefficientList[Series[(1+3x)/((1-x)(1-10x)),{x,0,20}],x] (* or *) LinearRecurrence[{11,-10},{1,14},20] (* or *) Table[FromDigits[PadRight[{1},n,4]],{n,20}] (* _Harvey P. Dale_, Mar 05 2023 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 30 2004