A187786 Table read by rows, where n-th row contains all numbers having in binary representation as many zeros and ones as n.

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, 13, 14, 15, 16, 17, 18, 20, 24, 17, 18, 20, 24, 19, 21, 22, 25, 26, 28, 17, 18, 20, 24, 19, 21, 22, 25, 26, 28, 19, 21, 22, 25, 26, 28, 23, 27, 29, 30, 17, 18, 20

Offset: 0

Author

Reinhard Zumkeller, Jan 06 2013

Keywords

• nonn
• base
• tabf
• look

Comments

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);

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

A187769 contains all rows without repetitions.

Examples

			.  n  n-th row              binary                          row length
. --  --------------------- ------------------------------- ----------
.  0  {0}                   {0}                                      1
.  1  {1}                   {1}                                      1
.  2  {2}                   {10}                                     1
.  3  {3}                   {11}                                     1
.  4  {4}                   {100}                                    1
.  5  {5,6}                 {101,110}                                2
.  6  {5,6}                 {101,110}                                2
.  7  {7}                   {111}                                    1
.  8  {8}                   {1000}                                   1
.  9  {9,10,12}             {1001,1010,1100}                         3
. 10  {9,10,12}             {1001,1010,1100}                         3
. 11  {11,13,14}            {1011,1101,1110}                         3
. 12  {9,10,12}             {1001,1010,1100}                         3
. 13  {11,13,14}            {1011,1101,1110}                         3
. 14  {11,13,14}            {1011,1101,1110}                         3
. 15  {15}                  {1111}                                   1
. 16  {16}                  {10000}                                  1
. 17  {17,18,20,24}         {10001,10010,10100,11000}                4
. 18  {17,18,20,24}         {10001,10010,10100,11000}                4
. 19  {19,21,22,25,26,28}   {10011,10101,10110,11001,11010,11100}    6
. 20  {17,18,20,24}         {10001,10010,10100,11000}                4 .
		

Links

• Reinhard Zumkeller, Rows n = 0..255 of triangle, flattened
• Index entries for sequences related to binary expansion of n

Programs

Haskell

import List (find)
import Maybe (fromJust)
a187786 n k = a187786_tabf !! n !! k
a187786_row n = fromJust $ find (elem n) a187769_tabf
a187786_tabf = map a187786_row [0..]