A175096 Write n in binary (without leading 0's). a(n) = the number of distinct numerical values made by permutating the runs of 0's and the runs of 1's, such that the runs (of nonzero length) of 1's alternate with the runs (of nonzero length) of 0's. The permutated binary numbers (those not equal to n) may start with leading 0's.

1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 4, 2, 4, 1, 4, 2, 2, 2, 4, 1, 2, 2, 2, 1, 2, 1, 4, 2, 2, 2, 8, 2, 4, 2, 2, 3, 8, 3, 4, 2, 2, 2, 8, 1, 8, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2, 1, 4, 2, 4, 2, 8, 2, 4, 1, 6, 6, 4, 6, 8, 2, 4, 2, 6, 6, 6, 1, 6, 3, 8, 6, 6, 3, 8, 3, 4, 2, 2, 2, 8, 1, 4, 6, 4, 2, 8, 6

Offset: 1

Author

Leroy Quet, Feb 01 2010

Keywords

• base
• nonn

Comments

Each "run" of binary digit b (0 or 1) is bounded by digits equal to 1-b, or is bounded by the edge of the binary string (which is n written in binary).

For all odd n, the values of all permutations of binary n are themselves odd, since there are an odd number of runs (the first and last runs being of 1's).

Examples

			20 in binary is 10100. So we have a run of one 1, followed by a run of one 0, followed by a run of one 1, followed finally by a run of two 0's. The permutations of the runs of 0's and the run's of 1's form these distinct binary numbers: 00101 (5 in decimal), 01001 (9 in decimal), 10010 (18 in decimal), and 10100 (20 in decimal). So a(20) = 4 since there are 4 such permutations.
		

Extensions

Extended by Ray Chandler, Feb 07 2010