|
%I #18 Dec 10 2017 18:49:06
%S 4,16,40,160,280,2176,2800,17920,44224,263296,419872,4280320,5594000,
%T 44751616,134391040,539054080,1073758360,11453771776,15271054960,
%U 137575813120,366528038400,1759220283904,3198580043440,35193817661440,56294998751872
%N Number of step shifted (decimated) sequences using a maximum of four different symbols.
%C See A056371 for an explanation of step shifts.
%D 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 G. C. Greubel, <a href="/A056373/b056373.txt">Table of n, a(n) for n = 1..1000</a>
%H 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 The cycle index is implicit in Titsworth.
%F 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 a[m_, n_] := (1/EulerPhi[n])*Sum[If[GCD[k, n] == 1, m^DivisorSum[n, EulerPhi[#]/MultiplicativeOrder[k, #] &], 0], {k, 1, n}]; Table[a[4, n], {n, 1, 25}] (* _Jean-François Alcover_, Dec 04 2015 *)
%Y Cf. A056412.
%Y A row or column of A132191.
%K nonn
%O 1,1
%A _Marks R. Nester_
%E More terms from _Max Alekseyev_, Nov 08 2007
|
