A045611 Number of different energy states of n positive and n negative charges on a necklace. Different sets of distances between n points chosen from 2n equally spaced points on a circle.

1, 1, 2, 3, 7, 13, 35, 85, 254, 701, 2377, 7944, 25220, 95910, 332300, 1164825, 4379920, 16649851, 58473414

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Sean A. Irvine, Java program (github)

Index entries for sequences related to necklaces

Example

a(10) = 2377 because the multiplicities {1; 2; 5; 10; 20; 40; 60; 80; 120} occur {1; 1; 3; 22; 362; 1855; 1; 130; 2} times and 2377 = 1 + 1 + 3 + 22 + 362 + 1855 + 1 + 130 + 2. Total number of configurations = 1*1 + 1*2 + 3*5 + 22*10 + .. = 92378 (see C(2n + 1, n + 1)=A001700).

Mathematica

n=4; perm=Permutations[ Table[ -1, {n-1} ]~Join~Table[ 1, {n} ] ]; res=Table[ (Prepend[ #, -1 ].RotateRight[ Prepend[ #, -1 ], k ])/2, {k, 1, n} ]&/@perm; kort=Length[ Length/@Split[ Sort[ res ] ] ]

Crossrefs

For n=0..7 this is equal to A006840. Cf. A045610, A045611, A045612, A006840, A077078, A077079.

Sequence in context: A056953 A371867 A321681 * A006840 A123408 A033995

Adjacent sequences: A045608 A045609 A045610 * A045612 A045613 A045614

Keyword

nonn,more

Author

Wouter Meeussen

Extensions

a(15) corrected and a(16)-a(18) from Sean A. Irvine, Mar 17 2021

Status

approved