A288620 Triangle read by rows: T(n,k) = number of step shifted (decimated) sequence structures of length n using exactly k different symbols.

1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 5, 8, 3, 1, 1, 19, 50, 37, 9, 1, 1, 13, 54, 63, 26, 4, 1, 1, 47, 284, 479, 299, 83, 11, 1, 1, 51, 525, 1316, 1183, 454, 82, 8, 1, 1, 139, 2370, 8597, 10701, 5761, 1492, 196, 13, 1, 1, 107, 2872, 14619, 24736, 17998, 6429, 1198, 119, 6, 1

Offset: 1

Author

Andrew Howroyd, Jun 11 2017

Keywords

• nonn
• tabl

Comments

See A056371 for an explanation of step shifts. Permuting the symbols will not change the structure.

Examples

			Triangle begins
1;
1,  1;
1,  2,   1;
1,  5,   4,    1;
1,  5,   8,    3,    1;
1, 19,  50,   37,    9,   1;
1, 13,  54,   63,   26,   4,  1;
1, 47, 284,  479,  299,  83, 11, 1;
1, 51, 525, 1316, 1183, 454, 82, 8, 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 A056396, A056397, A056398, A056399, A056400.

Row sums are A288621.

Partial row sums include A056391, A056392, A056393, A056394, A056395.

Cf. A056371, A288627, A285522, A285548, A132191.

Programs

PARI

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