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

1,5

Comments

See A056371 for an explanation of step shifts. 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

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

Example

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;
...

Prog

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

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.

Sequence in context: A076241 A316399 A139347 * A263324 A284949 A263294

Adjacent sequences: A288617 A288618 A288619 * A288621 A288622 A288623

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 11 2017

Status

approved