A056373 Number of step shifted (decimated) sequences using a maximum of four different symbols.

4, 16, 40, 160, 280, 2176, 2800, 17920, 44224, 263296, 419872, 4280320, 5594000, 44751616, 134391040, 539054080, 1073758360, 11453771776, 15271054960, 137575813120, 366528038400, 1759220283904, 3198580043440, 35193817661440, 56294998751872

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

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

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• R. C. Titsworth, Equivalence classes of periodic sequences, Illinois J. Math., 8 (1964), 266-270.

Crossrefs

Cf. A056412.

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[4, n], {n, 1, 25}] (* 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