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A288627
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Triangle read by rows: T(n,k) = number of step cyclic shifted sequence structures of length n using exactly k different symbols.
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11
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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
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1,8
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COMMENTS
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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.
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REFERENCES
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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]
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..1275
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EXAMPLE
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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;
...
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PROG
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(PARI) \\ see A056391 for Polya enumeration functions
T(n, k) = NonequivalentStructsExactly(CyclicStepShiftPerms(n), k); \\ Andrew Howroyd, Oct 14 2017
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CROSSREFS
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Columns 2-6 are A056434, A056435, A056436, A056437, A056438.
Row sums are A288628.
Partial row sums include A056429, A056430, A056431, A056432, A056433.
Cf. A056391, A056371, A288620, A285522, A285548, A132191.
Sequence in context: A172130 A202449 A326613 * A232096 A250030 A316456
Adjacent sequences: A288624 A288625 A288626 * A288628 A288629 A288630
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KEYWORD
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nonn,tabl
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AUTHOR
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Andrew Howroyd, Jun 11 2017
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STATUS
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approved
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