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Search: id:A056371
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| A056371 |
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Number of step shifted (decimated) sequences using a maximum of two different symbols. |
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82
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| 2, 4, 6, 12, 12, 40, 28, 96, 104, 280, 216, 1248, 704, 2800, 4344, 8928, 8232, 44224, 29204, 136032, 176752, 419872, 381492, 2150400, 1678256, 5594000, 7461168, 22553408, 19175160, 134391040, 71585136, 269510016, 429726240, 1073758360
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All step shifts of a sequence are considered to be equivalent, where a step shift transformation is obtained by selecting every k-th element of a sequence for some k relatively prime to n. For example, 2 is relatively prime to 5 and a 2-step shift of abcde is bdace.
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.
R. C. Titsworth, (1964). Equivalence classes of periodic sequences. Illinois J. Math. 8: 266-270.
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FORMULA
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The cycle index is implicit in Titsworth.
a(n) = ( SUM[k=1..n : gcd(k,n)=1] 2^(SUM[d|n] A000010(d)/ord_d(k)) ) / A000010(n), where ord_d(k) is the multiplicative order of k modulo d. - Max Alekseyev, Jun 18 2007, corrected Nov 08 2007
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PROGRAM
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(PARI) { a(n) = sum(k=1, n, if(gcd(k, n)==1, 2^sumdiv(n, d, eulerphi(d)/znorder(Mod(k, d))), 0); ) / eulerphi(n) } - Max Alekseyev, Jun 18 2007, corrected Nov 08 2007
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CROSSREFS
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Cf. A002729.
A row or column of A132191.
Sequence in context: A137387 A137394 A062856 this_sequence A067874 A015733 A023187
Adjacent sequences: A056368 A056369 A056370 this_sequence A056372 A056373 A056374
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KEYWORD
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nonn
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AUTHOR
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Marks R. Nester (nesterm(AT)dpi.qld.gov.au)
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EXTENSIONS
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More terms from Max Alekseyev, Jun 18 2007
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