A328035 Number of length n primitive (period n) bracelet structures which are not periodic palindromes using an infinite alphabet.

0, 0, 1, 2, 7, 23, 78, 311, 1297, 6200, 31747, 178703, 1070388, 6842898, 46158435, 327718768, 2437732593, 18948528721, 153498234770, 1293122838953, 11306474635818, 102425551817363, 959826751122645, 9290811889272509, 92771812680385087, 954447072777977556

Offset: 1

Author

Andrew Howroyd, Oct 02 2019

Keywords

• nonn

Comments

Equivalently, the number of length n bracelet structures that do not have any symmetry under the action of the dihedral group. The corresponding sequence for necklace structures that do not have any symmetry under the action of the cyclic group is A060223.

Examples

			For n = 5, the 7 bracelet structures have the patterns AAABC, AABAC, AABBC, ABABC, AABCD, ABACD, ABCDE.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Row sums of A309784.

Cf. A060223, A276548, A285042.

Programs

PARI

\\ Requires T from A309784.
seq(n)={my(A=T(n)); vector(n, i, vecsum(A[i, ]))}

Formula

a(n) = A276548(n) - A285042(n).