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

1,4

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.

Links

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

Formula

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

Example

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

Prog

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

Crossrefs

Row sums of A309784.

Cf. A060223, A276548, A285042.

Sequence in context: A274104 A068593 A198944 * A112657 A007717 A130567

Adjacent sequences: A328032 A328033 A328034 * A328036 A328037 A328038

Keyword

nonn

Author

Andrew Howroyd, Oct 02 2019

Status

approved