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

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

Author

Andrew Howroyd, Jun 11 2017

Keywords

• nonn
• tabl

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.

Examples

			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;
...
		

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

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

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.

Programs

PARI

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