A056372 Number of step shifted (decimated) sequences using a maximum of three different symbols.

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

Author

Marks R. Nester

Keywords

• nonn

Comments

See A056371 for an explanation of step shifts.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2000
• R. C. Titsworth, Equivalence classes of periodic sequences, Illinois J. Math., 8 (1964), 266-270.

Crossrefs

Cf. A056411.

A row or column of A132191.

Programs

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 *)

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

Extensions

More terms from Max Alekseyev, Nov 08 2007