A056430 -id:A056430 - cp's OEIS frontend

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

Andrew Howroyd, Jun 11 2017

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.

			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;
...

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 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.

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

A056440 Number of primitive (period n) step cyclic shifted sequence structures using a maximum of three different symbols.

Original entry on oeis.org

1, 1, 2, 4, 5, 18, 15, 60, 80, 293, 295, 2217, 1777, 9763, 20632, 58362, 79553, 600696, 567543, 3671674, 6935728, 23785615, 31017007, 246154210, 282456327, 1357925621, 2615206650, 11358502734

Offset: 1

Marks R. Nester

nonn

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.

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. A056420.

Sum mu(d)*A056430(n/d) where d divides n.

A056435 Number of step cyclic shifted sequence structures using exactly three different symbols.

Original entry on oeis.org

0, 0, 1, 2, 3, 14, 11, 52, 72, 274, 281, 2155, 1741, 9650, 20456, 58071, 79293, 599452, 566739, 3668218, 6931312, 23776154, 31008623, 246109051, 282422552, 1357819070, 2615067966, 11358104142

Offset: 1

Marks R. Nester

nonn

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.

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 A288627.

Cf. A056416.

A056430(n)-A056429(n).

A056436 Number of step cyclic shifted sequence structures using exactly four different symbols.

Original entry on oeis.org

0, 0, 0, 1, 1, 11, 13, 83, 162, 930, 1369, 13730, 16421, 124702, 355793, 1356781, 2555043, 25933814, 32931815, 283330733, 720489755, 3308255032, 5763641923, 60874698532, 93543112676, 600086810852

Offset: 1

Marks R. Nester

nonn

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.

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 A288627.

Cf. A056417.

A056431(n)-A056430(n).

cp's OEIS Frontend

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

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A056440 Number of primitive (period n) step cyclic shifted sequence structures using a maximum of three different symbols.

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A056435 Number of step cyclic shifted sequence structures using exactly three different symbols.

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A056436 Number of step cyclic shifted sequence structures using exactly four different symbols.

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