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A056375 Number of step shifted (decimated) sequences using a maximum of six different symbols. 8
6, 36, 126, 756, 2016, 23976, 46956, 435456, 1683576, 15128856, 36284472, 547204896, 1088416056, 13060989936, 58782164616, 352913845536, 1057916846196, 16926689693376, 33853322280036, 457078896068256, 1828085963706576 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A056371 for an explanation of step shifts.
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]
LINKS
R. C. Titsworth, Equivalence classes of periodic sequences, Illinois J. Math., 8 (1964), 266-270.
FORMULA
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
MATHEMATICA
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 *)
CROSSREFS
Cf. A056414.
A row or column of A132191.
Sequence in context: A061707 A253945 A331576 * A360588 A321579 A364429
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Max Alekseyev, Nov 08 2007
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)