A138118 - OEIS

%I #23 Jul 17 2026 13:40:52

%S 10,11100,11111000,11111110000,11111111100000,11111111111000000,

%T 11111111111110000000,11111111111111100000000,

%U 11111111111111111000000000,11111111111111111110000000000

%N Concatenation of 2n-1 digits 1 and n digits 0.

%C a(n) is also A147537(n) written in base 2. - _Omar E. Pol_, Nov 08 2008

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1010,-10000).

%F From _R. J. Mathar_, Apr 03 2008: (Start)

%F O.g.f.: 10*x*(1+100*x)/((-1+1000*x)*(-1+10*x)).

%F a(n) = A100706(n)*10^n.

%F a(n) = 10*a(n-1) + 11*1000^n. (End)

%F From _Elmo R. Oliveira_, Jul 17 2026: (Start)

%F a(n) = 10*A147589(n).

%F a(n) = 1010*a(n-1) - 10000*a(n-2) for n > 2.

%F E.g.f.: (9 - 10*exp(10*x) + exp(1000*x))/90. (End)

%e n .......... a(n)

%e 1 ........... 10

%e 2 ......... 11100

%e 3 ....... 11111000

%e 4 ..... 11111110000

%e 5 ... 11111111100000

%t FromDigits/@Table[Join[PadRight[{},2n-1,1],PadRight[{},n,0]],{n,15}] (* _Harvey P. Dale_, Dec 09 2011 *)

%Y Cf. A138147, A138721, A147537, A147589.

%K easy,nonn,base,changed

%O 1,1

%A _Omar E. Pol_, Mar 29 2008