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%I A056375 #18 Dec 01 2017 18:57:38
%S A056375 6,36,126,756,2016,23976,46956,435456,1683576,15128856,36284472,
%T A056375 547204896,1088416056,13060989936,58782164616,352913845536,
%U A056375 1057916846196,16926689693376,33853322280036,457078896068256,1828085963706576
%N A056375 Number of step shifted (decimated) sequences using a maximum of six different symbols.
%C A056375 See A056371 for an explanation of step shifts.
%D A056375 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]
%H A056375 G. C. Greubel, <a href="/A056375/b056375.txt">Table of n, a(n) for n = 1..1275</a>
%H A056375 R. C. Titsworth, <a href="http://projecteuclid.org/euclid.ijm/1256059671">Equivalence classes of periodic sequences</a>, Illinois J. Math., 8 (1964), 266-270.
%F A056375 The cycle index is implicit in Titsworth.
%F A056375 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
%t A056375 a[m_, n_] := (1/EulerPhi[n])*Sum[If[GCD[k, n] == 1, m^DivisorSum[n, EulerPhi[#]/MultiplicativeOrder[k, #] &], 0], {k, 1, n}]; Table[a[6, n], {n, 1, 21}] (* _Jean-François Alcover_, Dec 04 2015 *)
%Y A056375 Cf. A056414.
%Y A056375 A row or column of A132191.
%K A056375 nonn
%O A056375 1,1
%A A056375 _Marks R. Nester_
%E A056375 More terms from _Max Alekseyev_, Nov 08 2007

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