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.

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A056522 Number of primitive (period n) periodic palindromic structures using exactly five different symbols.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 15, 85, 140, 618, 1050, 4064, 6951, 24914, 42525, 145057, 246730, 814200, 1379400, 4446545, 7508501, 23798460, 40075034, 125435695, 210766920, 653516168, 1096190550, 3374551384, 5652751636, 17305626334, 28958095545, 88274117232
Offset: 1

Views

Author

Marks R. Nester

Keywords

Examples

			For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome. Permuting the symbols will not change the structure. This should be different from A056511.

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

Column 5 of A285037.
Cf. A056484, A056511, A056515, A056516.

Formula

a(n) = A056516(n) - A056515(n).
Moebius transform of A056511. - Andrew Howroyd, Oct 01 2019

Extensions

a(17)-a(28) from Andrew Howroyd, Apr 09 2017
Terms a(29) and beyond from Andrew Howroyd, Oct 01 2019

A056523 Number of primitive (period n) periodic palindromic structures using exactly six different symbols.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 13, 21, 154, 266, 1488, 2646, 12857, 22827, 101484, 179487, 752646, 1323652, 5325226, 9321312, 36387267, 63436373, 242085494, 420693273, 1577870839, 2734926558, 10120484024, 17505749897, 64096919293, 110687251039, 401885411487
Offset: 1

Views

Author

Marks R. Nester

Keywords

Examples

			For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome. Permuting the symbols will not change the structure. This should be different from A056512.

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

Column 6 of A285037.
Cf. A056485, A056512, A056516, A056517.

Formula

a(n) = A056517(n) - A056516(n).
Moebius transform of A056512. - Andrew Howroyd, Oct 01 2019

Extensions

a(16)-a(26) from Andrew Howroyd, Apr 09 2017
Terms a(27) and beyond from Andrew Howroyd, Oct 01 2019

A056518 Number of primitive (period n) periodic palindromic structures using exactly two different symbols.

Original entry on oeis.org

0, 1, 1, 2, 3, 4, 7, 10, 14, 21, 31, 42, 63, 91, 123, 184, 255, 371, 511, 750, 1015, 1519, 2047, 3030, 4092, 6111, 8176, 12222, 16383, 24486, 32767, 49024, 65503, 98175, 131061, 196308, 262143, 392959, 524223, 785910, 1048575, 1572256, 2097151, 3144702, 4194162
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome. 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 A285037.
Cf. A056481.

Formula

A056513(n)-A000007(n-1).

Extensions

a(17)-a(45) from Andrew Howroyd, Apr 08 2017
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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