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Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).
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%I #32 Mar 09 2024 11:12:33

%S 1,100,100111,1001110000,100111000011111,100111000011111000000,

%T 1001110000111110000001111111,100111000011111000000111111100000000,

%U 100111000011111000000111111100000000111111111,1001110000111110000001111111000000001111111110000000000

%N Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).

%C a(n) is divisible by A002275([(n+1)/2]) = (10^[(n+1)/2]-1)/9. Cf. A262806. - _Max Alekseyev_, Jun 02 2013

%C The unique sequence of binary words a(n) such that the k-th run of a(n) has length k, for k = 1..n . - _Clark Kimberling_, Mar 08 2024

%H Harry J. Smith, <a href="/A065447/b065447.txt">Table of n, a(n) for n = 1..44</a>

%e a(2) = 100, the concatenation of one 1, two 0's.

%e a(3) = 100111, the concatenation of one 1, two 0's, three 1's.

%e a(4) = 1001110000, the concatenation of one 1, two 0's, three 1's, four 0's.

%p a:= n-> parse(cat((irem(i,2)$i)$i=1..n)):

%p seq(a(n), n=1..10); # _Alois P. Heinz_, Mar 08 2024

%t FoldList[Join, {1}, Map[ConstantArray[Mod[#, 2], #] &, Range[2, 10]]] (* _Peter J. C. Moses_, Mar 08 2024 *)

%o (PARI) { m=10; for (n=1, 44, if (n==1, a=1, m*=10; a*=m; if (n%2, a+=(m - 1)/9)); write("b065447.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 19 2009

%Y For decimal version see A065760.

%Y Cf. A000217, A065761, A371032.

%K base,easy,nonn

%O 1,2

%A _Lior Manor_, Nov 18 2001