The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056412 Number of step cyclic shifted sequences using a maximum of four different symbols. 8
 4, 10, 20, 55, 76, 430, 460, 2605, 5164, 26962, 38572, 367645, 431780, 3203430, 8993804, 33860125, 63177820, 636462350, 803796700, 6886280971, 17456594380, 79965550558, 139069427020, 1466861706095, 2251803181492, 14434628481170, 37066691779180, 214483458079665, 354963555781060, 4803855154772166 (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 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, 4]]; cb, {n, 1, 30}] (* 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, 4), ", ")); \\ Joerg Arndt, Aug 27 2014 CROSSREFS Row 4 of A285548. Cf. A002729. Sequence in context: A019498 A237626 A020149 * A032275 A220828 A015220 Adjacent sequences: A056409 A056410 A056411 * A056413 A056414 A056415 KEYWORD nonn AUTHOR EXTENSIONS Added more terms, Joerg Arndt, Aug 27 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 29 15:46 EDT 2023. Contains 361599 sequences. (Running on oeis4.)