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

1,1

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[5, n], {n, 1, 23}] (* Jean-François Alcover, Dec 04 2015 *)

Crossrefs

Cf. A056413.

A row or column of A132191.

Sequence in context: A154286 A331575 A078234 * A301912 A171272 A366158

Adjacent sequences: A056371 A056372 A056373 * A056375 A056376 A056377

Keyword

nonn

Author

Marks R. Nester

Extensions

More terms from Max Alekseyev, Nov 08 2007

Status

approved