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Twice repdigit numbers.
1

%I #18 Jan 03 2024 22:09:01

%S 0,2,4,6,8,10,12,14,16,18,22,44,66,88,110,132,154,176,198,222,444,666,

%T 888,1110,1332,1554,1776,1998,2222,4444,6666,8888,11110,13332,15554,

%U 17776,19998,22222,44444,66666,88888,111110,133332,155554,177776,199998

%N Twice repdigit numbers.

%H Vincenzo Librandi, <a href="/A152966/b152966.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10).

%F a(n) = 2*A010785(n).

%F G.f.: 2*x*(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)*(10*x^9-1)). - _Colin Barker_, Sep 18 2013

%F a(n) = 11*a(n-9) - 10*a(n-18). - _Wesley Ivan Hurt_, Jan 03 2024

%t Join[{0},2*Flatten[Table[FromDigits[PadRight[{},n,d]],{n,5},{d,9}]]] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10},{0,2,4,6,8,10,12,14,16,18,22,44,66,88,110,132,154,176},50] (* _Harvey P. Dale_, Jun 20 2014 *)

%t CoefficientList[Series[2 x (9 x^8 + 8 x^7 + 7 x^6 + 6 x^5 + 5 x^4 + 4 x^3 + 3 x^2 + 2 x + 1)/((x - 1) (x^2 + x + 1) (x^6 + x^3 + 1) (10 x^9 - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 21 2014 *)

%Y Cf. A010785.

%K base,easy,nonn

%O 0,2

%A _Omar E. Pol_, Dec 16 2008