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Revision History for A056479

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Number of primitive (aperiodic) palindromic structures using a maximum of five different symbols.
(history; published version)

#10 by Alois P. Heinz at Wed Oct 02 17:45:38 EDT 2019

STATUS

proposed

approved

#9 by Andrew Howroyd at Wed Oct 02 13:08:46 EDT 2019

STATUS

editing

proposed

#8 by Andrew Howroyd at Wed Oct 02 12:41:30 EDT 2019

FORMULA

a(n) = Sum_{d|n} mu(d)*A056470(n/d) for n > 0.

#7 by Andrew Howroyd at Wed Oct 02 12:29:27 EDT 2019

DATA

1, 1, 0, 1, 1, 4, 3, 14, 13, 50, 47, 201, 196, 854, 840, 3839, 3830, 18001, 17947, 86471, 86419, 421989, 421803, 2079474, 2079260, 10306747, 10305897, 51263890, 51263086, 255514354, 255510460, 1275163904, 1275160060, 6368612099, 6368594300, 31821472593, 31821454413

OFFSET

1,5

0,6

LINKS

Andrew Howroyd, <a href="/A056479/b056479.txt">Table of n, a(n) for n = 0..500</a>

FORMULA

a(n) = Sum _{d|n} mu(d)*A056470(n/d) where d|n.

a(n) = Sum_{k=1..5} A284826(n, k) for n > 0. - Andrew Howroyd, Oct 02 2019

CROSSREFS

Cf. A056461, A056470, A284826.

EXTENSIONS

a(0)=1 prepended and terms a(32) and beyond from Andrew Howroyd, Oct 02 2019

STATUS

approved

editing

#6 by N. J. A. Sloane at Tue Aug 22 20:53:13 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 10:39:37 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 (aperiodic) palindromic structures using a maximum of five different characterssymbols.

COMMENTS

Permuting the characters symbols will not change the structure.

KEYWORD

nonn,new

nonn

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

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)*A056470(n/d) where d|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 (aperiodic) palindromic structures using a maximum of five different characters.

DATA

1, 0, 1, 1, 4, 3, 14, 13, 50, 47, 201, 196, 854, 840, 3839, 3830, 18001, 17947, 86471, 86419, 421989, 421803, 2079474, 2079260, 10306747, 10305897, 51263890, 51263086, 255514354, 255510460, 1275163904

OFFSET

1,5

COMMENTS

Permuting the characters 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)*A056470(n/d) where d|n.

CROSSREFS

Cf. A056461.

KEYWORD

nonn

AUTHOR

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

STATUS

approved