A077078 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	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.`
	EXAMPLE	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.` `Sequence in context: A143658 A005230 A030037 * A077079 A079969 A034064` `Adjacent sequences: A077075 A077076 A077077 * A077079 A077080 A077081`
	KEYWORD	`hard,more,nonn`
	AUTHOR	`Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 27 2002`

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Last modified February 14 10:24 EST 2012. Contains 205614 sequences.