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A056374 Number of step shifted (decimated) sequences using a maximum of five different symbols. 5
5, 25, 75, 375, 825, 8125, 13175, 103125, 327125, 2445625, 4884435, 61640625, 101732425, 1017323125, 3816215625, 19104609375, 47683838325, 635787765625, 1059638680675, 11924780390625, 39736963221875, 238418603522125, 541860418146375 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..23.

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-Fran├žois Alcover, Dec 04 2015 *)

CROSSREFS

Cf. A056413.

A row or column of A132191.

Sequence in context: A147130 A154286 A078234 * A171272 A243303 A238449

Adjacent sequences:  A056371 A056372 A056373 * A056375 A056376 A056377

KEYWORD

nonn

AUTHOR

Marks R. Nester (nesterm(AT)dpi.qld.gov.au)

EXTENSIONS

More terms from Max Alekseyev, Nov 08 2007

STATUS

approved

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Last modified December 5 03:30 EST 2016. Contains 278755 sequences.