A056369
Number of primitive (period n) bracelet structures using exactly five different colored beads.
Original entry on oeis.org
0, 0, 0, 0, 1, 3, 16, 85, 434, 2270, 11530, 58397, 290689, 1436669, 7036417, 34286379, 166316979, 804556969, 3884248150, 18731031687, 90269841908, 434955103451, 2096028083116, 10104206843502
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056370
Number of primitive (period n) bracelet structures using exactly six different colored beads.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 3, 27, 171, 1249, 8389, 56078, 360430, 2272598, 14037552, 85516427, 514976658, 3074986236, 18239677629, 107654218055, 632996894925, 3711499485032, 21716765203045, 126880009551584
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A276548
Number of primitive (period n) bracelet structures using an infinite alphabet.
Original entry on oeis.org
1, 1, 2, 5, 11, 33, 92, 347, 1347, 6338, 31949, 179265, 1071264, 6845487, 46162569, 327731596, 2437753739, 18948597836, 153498350744, 1293123237572, 11306475314372, 102425554267565, 959826755336241, 9290811905211847
Offset: 1
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u[0, ] = 1; u[k, j_] := u[k, j] = Sum[Binomial[k - 1, i - 1] Total[u[k - i, j] #^(i - 1) & /@ Divisors[j]], {i, k}];
b[n_] := 1/n*Total[EulerPhi[#] u[Quotient[n, #], #]& /@ Divisors[n] ];
A084708[n_] := b[n]/2 + If[EvenQ[n], u[n/2, 2], Sum[Binomial[n/2 - 1/2, k] u[k, 2], {k, 0, n/2 - 1/2}]]/2;
a[n_] := Sum[MoebiusMu[n/d]*A084708[d], {d, Divisors[n]}];
Array[a, 24] (* Jean-François Alcover, Dec 28 2017, after Andrew Howroyd and Wouter Meeussen *)
A056366
Number of primitive (period n) bracelet structures using exactly two different colored beads.
Original entry on oeis.org
0, 1, 1, 2, 3, 5, 8, 14, 21, 39, 62, 112, 189, 352, 607, 1144, 2055, 3885, 7154, 13602, 25472, 48670, 92204, 176770, 337590, 649341, 1246840, 2404872, 4636389, 8964143, 17334800
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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