The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A056362 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A056362

Number of primitive (period n) bracelet structures using a maximum of three different colored beads.
(history; published version)

#10 by Alois P. Heinz at Sat Oct 26 14:28:34 EDT 2019

STATUS

proposed

approved

#9 by Andrew Howroyd at Sat Oct 26 13:36:53 EDT 2019

STATUS

editing

proposed

#8 by Andrew Howroyd at Sat Oct 26 13:22:04 EDT 2019

FORMULA

a(n) = Sum_{d|n} mu(d)*A056353(n/d) for n > 0.

#7 by Andrew Howroyd at Sat Oct 26 13:15:39 EDT 2019

DATA

1, 1, 1, 2, 4, 8, 18, 39, 94, 222, 572, 1463, 3934, 10584, 29211, 80808, 226430, 636320, 1800318, 5107479, 14548360, 41538874, 118927919, 341187047, 980838750, 2824561080, 8147547156, 23536592010, 68087313892, 197216119544, 571924673368, 1660419530055, 4825587979390

OFFSET

1,3

0,4

LINKS

Andrew Howroyd, <a href="/A056362/b056362.txt">Table of n, a(n) for n = 0..200</a>

FORMULA

a(n) = Sum _{d|n} mu(d)*A056353(n/d) where d divides n.

a(n) = Sum_{k=1..3} A276543(n, k) for n > 0. - Andrew Howroyd, Oct 26 2019

CROSSREFS

Cf. A002075, A056353, A056367, A276543.

EXTENSIONS

a(0)=1 prepended and terms a(28) and beyond from Andrew Howroyd, Oct 26 2019

STATUS

approved

editing

#6 by N. J. A. Sloane at Tue Aug 22 20:53:09 EDT 2017

AUTHOR

Marks R. Nester (nesterm(AT)dpi.qld.gov.au)

Marks R. Nester

Discussion

Tue Aug 22

20:53

OEIS Server: https://oeis.org/edit/global/2696

#5 by N. J. A. Sloane at Fri May 19 10:39:28 EDT 2017

REFERENCES

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]

Discussion

Fri May 19

10:39

OEIS Server: https://oeis.org/edit/global/2652

#4 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

KEYWORD

nonn,new

nonn

AUTHOR

Marks R. Nester (nesterm(AT)qfri1.se2.dpi.qld.gov.au)

#3 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

NAME

Primitive Number of primitive (period n) bracelet structures using a maximum of three different colored beads.

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Primitive (period n) bracelet structures using a maximum of three different coloured colored beads.

COMMENTS

Turning over will not create a new bracelet. Permuting the colours colors of the beads will not change the structure.

REFERENCES

M. R. Nester, M. R. (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.

FORMULA

sum mobiusSum mu(d)*A056353(n/d) where d| divides n.

KEYWORD

nonn,new

nonn

AUTHOR

Marks R. Nester (nesterm@(AT)qfri1.se2.dpi.qld.gov.au)

#1 by N. J. A. Sloane at Sat Jul 22 03:00:00 EDT 2000

NAME

Primitive (period n) bracelet structures using a maximum of three different coloured beads.

DATA

1, 1, 2, 4, 8, 18, 39, 94, 222, 572, 1463, 3934, 10584, 29211, 80808, 226430, 636320, 1800318, 5107479, 14548360, 41538874, 118927919, 341187047, 980838750, 2824561080, 8147547156, 23536592010

OFFSET

1,3

COMMENTS

Turning over will not create a new bracelet. Permuting the colours of the beads will not change the structure.

REFERENCES

Nester, M. R. (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.

FORMULA

sum mobius(d)*A056353(n/d) where d|n.

CROSSREFS

Cf. A002075.

KEYWORD

nonn

AUTHOR

Marks R. Nester (nesterm@qfri1.se2.dpi.qld.gov.au)

STATUS

approved