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A056375
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Number of step shifted (decimated) sequences using a maximum of six different symbols.
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8
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6, 36, 126, 756, 2016, 23976, 46956, 435456, 1683576, 15128856, 36284472, 547204896, 1088416056, 13060989936, 58782164616, 352913845536, 1057916846196, 16926689693376, 33853322280036, 457078896068256, 1828085963706576
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OFFSET
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1,1
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COMMENTS
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See A056371 for an explanation of step shifts.
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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. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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The cycle index is implicit in Titsworth.
Sequences A056372-A056375 fit a general formula, implemented in PARI/GP as follows: { a(m,n) = sum(k=1, n, if(gcd(k, n)==1, m^sumdiv(n, d, eulerphi(d)/znorder(Mod(k, d))), 0); ) / eulerphi(n) }. - Max Alekseyev, Nov 08 2007
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MATHEMATICA
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a[m_, n_] := (1/EulerPhi[n])*Sum[If[GCD[k, n] == 1, m^DivisorSum[n, EulerPhi[#]/MultiplicativeOrder[k, #] &], 0], {k, 1, n}]; Table[a[6, n], {n, 1, 21}] (* Jean-François Alcover, Dec 04 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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