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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
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
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
Columns 2-6 are A056434, A056435, A056436, A056437, A056438.
Row sums are A288628.
Partial row sums include A056429, A056430, A056431, A056432, A056433.
Sequence in context: A172130 A202449 A326613 * A232096 A250030 A316456
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jun 11 2017
STATUS
approved