

A288627


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


11



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, 83, 52, 18, 3, 1, 1, 10, 72, 162, 148, 59, 13, 2, 1, 1, 25, 274, 930, 1140, 630, 171, 28, 3, 1, 1, 14, 281, 1369, 2306, 1681, 612, 118, 14, 1, 1
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OFFSET

1,8


COMMENTS

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.


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



EXAMPLE

Triangle begins
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, 83, 52, 18, 3, 1;
1, 10, 72, 162, 148, 59, 13, 2, 1;
1, 25, 274, 930, 1140, 630, 171, 28, 3, 1;
...


PROG

(PARI) \\ see A056391 for Polya enumeration functions
T(n, k) = NonequivalentStructsExactly(CyclicStepShiftPerms(n), k); \\ Andrew Howroyd, Oct 14 2017


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



