A056374 Number of step shifted (decimated) sequences using a maximum of five different symbols.

5, 25, 75, 375, 825, 8125, 13175, 103125, 327125, 2445625, 4884435, 61640625, 101732425, 1017323125, 3816215625, 19104609375, 47683838325, 635787765625, 1059638680675, 11924780390625, 39736963221875, 238418603522125, 541860418146375

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. A056413.

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[5, n], {n, 1, 23}] (* 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