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A288627 Triangle read by rows: T(n,k) = number of step cyclic shifted sequence structures of length n using exactly k different symbols.

%I A288627 #10 Oct 16 2017 02:34:07
%S A288627 1,1,1,1,1,1,1,3,2,1,1,2,3,1,1,1,7,14,11,3,1,1,4,11,13,6,1,1,1,13,52,
%T A288627 83,52,18,3,1,1,10,72,162,148,59,13,2,1,1,25,274,930,1140,630,171,28,
%U A288627 3,1,1,14,281,1369,2306,1681,612,118,14,1,1
%N A288627 Triangle read by rows: T(n,k) = number of step cyclic shifted sequence structures of length n using exactly k different symbols.
%C A288627 See A056371 for an explanation of step shifts. Under step cyclic shifts, abcde, bdace, bcdea, cdeab and daceb etc. are equivalent. Permuting the symbols will not change the structure.
%D A288627 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 A288627 Andrew Howroyd, <a href="/A288627/b288627.txt">Table of n, a(n) for n = 1..1275</a>
%e A288627 Triangle begins
%e A288627 1;
%e A288627 1,  1;
%e A288627 1,  1,   1;
%e A288627 1,  3,   2,   1;
%e A288627 1,  2,   3,   1,    1;
%e A288627 1,  7,  14,  11,    3,   1;
%e A288627 1,  4,  11,  13,    6,   1,   1;
%e A288627 1, 13,  52,  83,   52,  18,   3,  1;
%e A288627 1, 10,  72, 162,  148,  59,  13,  2, 1;
%e A288627 1, 25, 274, 930, 1140, 630, 171, 28, 3, 1;
%e A288627 ...
%o A288627 (PARI) \\ see A056391 for Polya enumeration functions
%o A288627 T(n,k) = NonequivalentStructsExactly(CyclicStepShiftPerms(n), k); \\ _Andrew Howroyd_, Oct 14 2017
%Y A288627 Columns 2-6 are A056434, A056435, A056436, A056437, A056438.
%Y A288627 Row sums are A288628.
%Y A288627 Partial row sums include A056429, A056430, A056431, A056432, A056433.
%Y A288627 Cf. A056391, A056371, A288620, A285522, A285548, A132191.
%K A288627 nonn,tabl
%O A288627 1,8
%A A288627 _Andrew Howroyd_, Jun 11 2017