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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. 11

%I

%S 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 83,52,18,3,1,1,10,72,162,148,59,13,2,1,1,25,274,930,1140,630,171,28,

%U 3,1,1,14,281,1369,2306,1681,612,118,14,1,1

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

%C 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 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 Andrew Howroyd, <a href="/A288627/b288627.txt">Table of n, a(n) for n = 1..1275</a>

%e Triangle begins

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 3, 2, 1;

%e 1, 2, 3, 1, 1;

%e 1, 7, 14, 11, 3, 1;

%e 1, 4, 11, 13, 6, 1, 1;

%e 1, 13, 52, 83, 52, 18, 3, 1;

%e 1, 10, 72, 162, 148, 59, 13, 2, 1;

%e 1, 25, 274, 930, 1140, 630, 171, 28, 3, 1;

%e ...

%o (PARI) \\ see A056391 for Polya enumeration functions

%o T(n,k) = NonequivalentStructsExactly(CyclicStepShiftPerms(n), k); \\ _Andrew Howroyd_, Oct 14 2017

%Y Columns 2-6 are A056434, A056435, A056436, A056437, A056438.

%Y Row sums are A288628.

%Y Partial row sums include A056429, A056430, A056431, A056432, A056433.

%Y Cf. A056391, A056371, A288620, A285522, A285548, A132191.

%K nonn,tabl

%O 1,8

%A _Andrew Howroyd_, Jun 11 2017

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Last modified March 2 06:13 EST 2021. Contains 341742 sequences. (Running on oeis4.)