A077078 Number of different absolute values of vector sums generated by n vectors chosen from 2n (equally spaced) points around the unit circle. Dipole moments of n positive and n negative equally spaced charges on a circle.

1, 2, 3, 6, 11, 20, 53, 130, 196, 725, 1990, 2437, 14466, 38697, 18878

Offset: 1

Author

Wouter Meeussen, Oct 27 2002

Keywords

• hard
• more
• nonn

Comments

Starting from n ones and n zero's cf. A006840, the simplification can remove subsets of ones with vector sum equal to zero, thus lowering the count of ones in the simplified bracelet.

The count is lower than A077079 because the absolute vector sums can be equal without being symmetrically related.

Examples

			The 35 bracelets for n=6 simplify to the following 20: {0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,1}, {0,0,0,0,0,0,0,0,0,0,1,1}, {0,0,0,0,0,0,0,0,0,1,0,1}, {0,0,0,0,0,0,0,0,0,1,1,1}, {0,0,0,0,0,0,0,0,1,0,0,1}, {0,0,0,0,0,0,0,0,1,0,1,1}, {0,0,0,0,0,0,0,0,1,1,1,1}, {0,0,0,0,0,0,0,1,0,1,0,1}, {0,0,0,0,0,0,0,1,0,1,1,1}, {0,0,0,0,0,0,1,0,0,0,0,1}, {0,0,0,0,0,0,1,0,0,1,0,1}, {0,0,0,0,0,0,1,0,1,0,1,1}, {0,0,0,0,0,0,1,0,1,1,0,1}, {0,0,0,0,0,0,1,1,1,1,1,1}, {0,0,0,0,1,0,0,0,0,1,0,1}, {0,0,0,0,1,0,0,1,0,1,0,1}, {0,0,0,0,1,0,1,0,0,1,0,1}, {0,0,0,0,1,0,1,1,1,1,0,1}, {0,0,1,0,1,0,1,1,0,1,0,1}
		

Crossrefs

Cf. A077079, A006840.