cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

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

Original entry on oeis.org

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

Views

Author

Andrew Howroyd, Jun 11 2017

Keywords

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

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

A056429 Number of step cyclic shifted sequence structures using a maximum of two different symbols.

Original entry on oeis.org

1, 2, 2, 4, 3, 8, 5, 14, 11, 26, 15, 88, 37, 130, 184, 357, 261, 1346, 805, 3760, 4434, 9758, 8385, 47462, 33781, 108330, 138767, 408376, 331185, 2251816, 1155735
Offset: 1

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Cf. A002729, A288627.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.
a(n) = A288627(n, 2) + 1. - Andrew Howroyd, Jun 13 2017

A056430 Number of step cyclic shifted sequence structures using a maximum of three different symbols.

Original entry on oeis.org

1, 2, 3, 6, 6, 22, 16, 66, 83, 300, 296, 2243, 1778, 9780, 20640, 58428, 79554, 600798, 567544, 3671978, 6935746, 23785912, 31017008, 246156513, 282456333, 1357927400, 2615206733, 11358512518
Offset: 1

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Cf. A056411, A288627.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.
a(n) = Sum_{k=1..3} A288627(n, k). - Andrew Howroyd, Jun 13 2017

A056431 Number of step cyclic shifted sequence structures using a maximum of four different symbols.

Original entry on oeis.org

1, 2, 3, 7, 7, 33, 29, 149, 245, 1230, 1665, 15973, 18199, 134482, 376433, 1415209, 2634597, 26534612, 33499359, 287002711, 727425501, 3332040944, 5794658931, 61120855045, 93825569009, 601444738252
Offset: 1

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Cf. A056412, A288627.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.
a(n) = Sum_{k=1..4} A288627(n, k). - Andrew Howroyd, Jun 13 2017

A288628 Number of step cyclic shifted sequence structures of length n using an infinite alphabet.

Original entry on oeis.org

1, 2, 3, 7, 8, 37, 37, 223, 468, 3203, 6398, 93103, 178663, 2282131, 11561896, 82120878, 304719416, 6316222138, 17055376113, 323332552319, 1884432112761, 20485110860448, 87256977757852, 2322728266726152, 9277181270824996, 159074512149044084, 1122874592283076868
Offset: 1

Views

Author

Andrew Howroyd, Jun 11 2017

Keywords

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.

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]

Crossrefs

Row sums of A288627.
Cf. A056391, A056371, A288621.

Programs

  • PARI
    \\ see A056391 for Polya enumeration functions
a(n) = NonequivalentStructs(CyclicStepShiftPerms(n), n); \\ Andrew Howroyd, Oct 14 2017

A056434 Number of step cyclic shifted sequence structures using exactly two different symbols.

Original entry on oeis.org

0, 1, 1, 3, 2, 7, 4, 13, 10, 25, 14, 87, 36, 129, 183, 356, 260, 1345, 804, 3759, 4433, 9757, 8384, 47461, 33780, 108329, 138766, 408375, 331184, 2251815, 1155734
Offset: 1

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Column 2 of A288627.
Cf. A056415.

Formula

A056429(n)-1.

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

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Column 3 of A288627.
Cf. A056416.

Formula

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

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Column 4 of A288627.
Cf. A056417.

Formula

A056431(n)-A056430(n).

A056437 Number of step cyclic shifted sequence structures using exactly five different symbols.

Original entry on oeis.org

0, 0, 0, 0, 1, 3, 6, 52, 148, 1140, 2306, 30121, 48476, 478957, 1762917, 8601630, 20789656, 268188642, 431583572, 4685759111, 15045763312, 86991023001, 190548007556, 2526401808203, 4873374476388, 39199367162137
Offset: 1

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Column 5 of A288627.
Cf. A056418.

Formula

A056432(n)-A056431(n).

A056438 Number of step cyclic shifted sequence structures using exactly six different symbols.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 18, 59, 630, 1681, 28867, 60083, 757577, 3514504, 21424002, 64372109, 1024999230, 2026631203, 26920955243, 105501588415, 742299898741, 1974251382095, 31721456317841, 74052852505684
Offset: 1

Views

Author

Marks R. Nester

Keywords

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.

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]

Crossrefs

Column 6 of A288627.
Cf. A056419.

Formula

A056433(n)-A056432(n).
Showing 1-10 of 10 results.

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