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 A056374 Number of step shifted (decimated) sequences using a maximum of five different symbols. 6
 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. [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 A243303 Adjacent sequences: A056371 A056372 A056373 * A056375 A056376 A056377 KEYWORD nonn AUTHOR EXTENSIONS More terms from Max Alekseyev, Nov 08 2007 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)