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

1,1

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

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.

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[4, n], {n, 1, 25}] (* Jean-François Alcover, Dec 04 2015 *)

Crossrefs

Cf. A056412.

A row or column of A132191.

Sequence in context: A110477 A007057 A206918 * A018828 A323847 A114211

Adjacent sequences: A056370 A056371 A056372 * A056374 A056375 A056376

Keyword

nonn

Author

Marks R. Nester

Extensions

More terms from Max Alekseyev, Nov 08 2007

Status

approved