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A056372
Number of step shifted (decimated) sequences using a maximum of three different symbols.
11
3, 9, 18, 54, 72, 405, 390, 1944, 3411, 14985, 17802, 139968, 133104, 798525, 1804518, 5454378, 8072532, 64599849, 64573626, 437732424, 872157294, 3138159429, 4279259574, 35362084140, 42364514403, 211822562025, 423646166250
OFFSET
1,1
COMMENTS
See A056371 for an explanation of step shifts.
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[3, n], {n, 1, 27}] (* Jean-François Alcover, Dec 04 2015 *)
CROSSREFS
Cf. A056411.
A row or column of A132191.
Sequence in context: A027101 A015656 A188797 * A181574 A101652 A026565
KEYWORD
nonn
EXTENSIONS
More terms from Max Alekseyev, Nov 08 2007
STATUS
approved