A056392 -id:A056392 - cp's OEIS frontend

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

Andrew Howroyd, Jun 11 2017

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

			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;
...

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]

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

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.

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

A056402 Number of primitive (aperiodic) step shifted (decimated) sequence structures using a maximum of three different symbols.

Original entry on oeis.org

1, 1, 3, 8, 13, 65, 67, 322, 573, 2495, 2979, 23294, 22217, 133081, 300947, 909050, 1345633, 10766559, 10762819, 72954582, 145362861, 523026545, 713213955, 5893685746, 7060765719, 35303760331

Offset: 1

Marks R. Nester

nonn

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

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]

Cf. A056382.

Sum mu(d)*A056392(n/d) where d|n.

A056397 Number of step shifted (decimated) sequence structures using exactly three different symbols.

Original entry on oeis.org

0, 0, 1, 4, 8, 50, 54, 284, 525, 2370, 2872, 22748, 21866, 131750, 298792, 904918, 1341518, 10745090, 10748218, 72889084, 145274556, 522819590, 713023210, 5892634240, 7059926605, 35300985550, 70604008204

Offset: 1

Marks R. Nester

nonn

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

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]

Column 3 of A288620.

Cf. A056377.

A056392(n)-A056391(n).

A056398 Number of step shifted (decimated) sequence structures using exactly four different symbols.

Original entry on oeis.org

0, 0, 0, 1, 3, 37, 63, 479, 1316, 8597, 14619, 155999, 211231, 1732907, 5302823, 21559909, 43398413, 466495335, 625545865, 5659500031, 15126813765, 72778025365, 132561145173, 1460519554091, 2338565021382

Offset: 1

Marks R. Nester

nonn

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

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]

Column 4 of A288620.

Cf. A056378.

A056393(n)-A056392(n).

cp's OEIS Frontend

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

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A056402 Number of primitive (aperiodic) step shifted (decimated) sequence structures using a maximum of three different symbols.

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A056397 Number of step shifted (decimated) sequence structures using exactly three different symbols.

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A056398 Number of step shifted (decimated) sequence structures using exactly four different symbols.

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