A138118 Concatenation of 2n-1 digits 1 and n digits 0.

10, 11100, 11111000, 11111110000, 11111111100000, 11111111111000000, 11111111111110000000, 11111111111111100000000, 11111111111111111000000000, 11111111111111111110000000000

Offset

1,1

Comments

a(n) is also A147537(n) written in base 2. - Omar E. Pol, Nov 08 2008

Links

Table of n, a(n) for n=1..10.

Index entries for linear recurrences with constant coefficients, signature (1010,-10000).

Formula

From R. J. Mathar, Apr 03 2008: (Start)

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

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

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

From Elmo R. Oliveira, Jul 17 2026: (Start)

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

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

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

Example

n .......... a(n)
1 ........... 10
2 ......... 11100
3 ....... 11111000
4 ..... 11111110000
5 ... 11111111100000

Mathematica

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

Crossrefs

Cf. A138147, A138721, A147537, A147589.

Sequence in context: A086164 A138119 A327233 * A267130 A267850 A267206

Adjacent sequences: A138115 A138116 A138117 * A138119 A138120 A138121

Keyword

easy,nonn,base,changed

Author

Omar E. Pol, Mar 29 2008

Status

approved