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 A056414 Number of step cyclic shifted sequences using a maximum of six different symbols. 6
 6, 21, 56, 231, 462, 4291, 6966, 57561, 188866, 1519035, 3302922, 45921281, 83747286, 933081411, 3920355712, 22075451286, 62230996506, 940379310731, 1781757016326, 22856965214727, 87052415641136, 598280600648031, 1560731765058606, 24680195365765751, 56860576713326910, 546736312124316741, 2105947271634851386 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A056371 for an explanation of step shifts. Under step cyclic shifts, abcde, bdace, bcdea, cdeab and daceb etc. are equivalent. 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 Table of n, a(n) for n=1..27. D. Z. Dokovic, I. Kotsireas et al., Charm bracelets and their application to the construction of periodic Golay pairs, arXiv:1405.7328 [math.CO], 2014. R. C. Titsworth, Equivalence classes of periodic sequences, Illinois J. Math., 8 (1964), 266-270. FORMULA Refer to Titsworth or slight "simplification" in Nester. MATHEMATICA M[j_, L_] := Module[{m = 1}, While[Sum[ j^i, {i, 0, m - 1}] ~Mod~ L != 0, m++]; m]; c[j_, t_, n_] := Sum[ 1/M[j, n / GCD[n, u*(j - 1) + t] ], {u, 0, n - 1}]; CB[n_, k_] = If[n == 1, k, 1/(n*EulerPhi[n]) * Sum[ If[1 == GCD[n, j], k^c[j, t, n], 0], {t, 0, n-1}, {j, 1, n-1}]]; Table[ Print[ cb = CB[n, 6]]; cb, {n, 1, 27}] (* Jean-François Alcover, Dec 04 2015, after Joerg Arndt *) PROG (PARI) \\ see p.3 of the Dokovic et al. reference M(j, L)={my(m=1); while ( sum(i=0, m-1, j^i) % L != 0, m+=1 ); m; } c(j, t, n)=sum(u=0, n-1, 1/M(j, n / gcd(n, u*(j-1)+t) ) ); CB(n, k)=if (n==1, k, 1/(n*eulerphi(n)) * sum(t=0, n-1, sum(j=1, n-1, if(1==gcd(n, j), k^c(j, t, n), 0) ) ) ); for(n=1, 66, print1(CB(n, 6), ", ")); \\ Joerg Arndt, Aug 27 2014 CROSSREFS Row 6 of A285548. Cf. A002729. Sequence in context: A247904 A074745 A296821 * A056341 A144899 A053809 Adjacent sequences: A056411 A056412 A056413 * A056415 A056416 A056417 KEYWORD nonn AUTHOR Marks R. Nester EXTENSIONS Added more terms, Joerg Arndt, Aug 27 2014 STATUS approved

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Last modified May 29 13:20 EDT 2023. Contains 363042 sequences. (Running on oeis4.)