%I #12 Jan 29 2014 04:03:43

%S 0,1,2,3,4,5,6,5,6,7,8,9,10,12,9,10,12,11,13,14,9,10,12,11,13,14,11,

%T 13,14,15,16,17,18,20,24,17,18,20,24,19,21,22,25,26,28,17,18,20,24,19,

%U 21,22,25,26,28,19,21,22,25,26,28,23,27,29,30,17,18,20

%N Table read by rows, where n-th row contains all numbers having in binary representation as many zeros and ones as n.

%C For k = 0..A090706(n)-1: A023416(T(n,k))=A023416(n); A000120(T(n,k))=A000120(n); A053644(n)<=T(n,k)<=A003817(n);

%C T(n,k) = n for some k;

%C A187769 contains all rows without repetitions.

%H Reinhard Zumkeller, <a href="/A187786/b187786.txt">Rows n = 0..255 of triangle, flattened</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e . n n-th row binary row length

%e . -- --------------------- ------------------------------- ----------

%e . 0 {0} {0} 1

%e . 1 {1} {1} 1

%e . 2 {2} {10} 1

%e . 3 {3} {11} 1

%e . 4 {4} {100} 1

%e . 5 {5,6} {101,110} 2

%e . 6 {5,6} {101,110} 2

%e . 7 {7} {111} 1

%e . 8 {8} {1000} 1

%e . 9 {9,10,12} {1001,1010,1100} 3

%e . 10 {9,10,12} {1001,1010,1100} 3

%e . 11 {11,13,14} {1011,1101,1110} 3

%e . 12 {9,10,12} {1001,1010,1100} 3

%e . 13 {11,13,14} {1011,1101,1110} 3

%e . 14 {11,13,14} {1011,1101,1110} 3

%e . 15 {15} {1111} 1

%e . 16 {16} {10000} 1

%e . 17 {17,18,20,24} {10001,10010,10100,11000} 4

%e . 18 {17,18,20,24} {10001,10010,10100,11000} 4

%e . 19 {19,21,22,25,26,28} {10011,10101,10110,11001,11010,11100} 6

%e . 20 {17,18,20,24} {10001,10010,10100,11000} 4 .

%o (Haskell)

%o import List (find)

%o import Maybe (fromJust)

%o a187786 n k = a187786_tabf !! n !! k

%o a187786_row n = fromJust $ find (elem n) a187769_tabf

%o a187786_tabf = map a187786_row [0..]

%K nonn,base,tabf,look

%O 0,3

%A _Reinhard Zumkeller_, Jan 06 2013