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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A056511 Number of periodic palindromic structures of length n 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, 4065, 6951, 24915, 42525, 145067, 246730, 814215, 1379400, 4446631, 7508501, 23798600, 40075035, 125436313, 210766920, 653517228, 1096190550, 3374555449, 5652751651, 17305633285, 28958095545, 88274142232
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.

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 A285012.
Cf. A056474, A056505, A056506, A056522.

Formula

a(n) = A056506(n) - A056505(n).
Inverse Moebius transform of A056522. - Andrew Howroyd, Oct 01 2019

Extensions

a(17)-a(28) from Andrew Howroyd, Apr 07 2017
Terms a(29) and beyond from Andrew Howroyd, Oct 01 2019

A056512 Number of periodic palindromic structures of length n 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, 101485, 179487, 752647, 1323652, 5325239, 9321312, 36387288, 63436373, 242085648, 420693273, 1577871106, 2734926558, 10120485512, 17505749898, 64096921939, 110687251039, 401885424357
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.

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 k=6 of A285012.
Cf. A056475, A056506, A056507, A056523.

Formula

a(n) = A056507(n) - A056506(n).
Inverse Moebius transform of A056523. - Andrew Howroyd, Oct 01 2019

Extensions

a(16)-a(26) from Andrew Howroyd, Apr 07 2017
Terms a(27) and beyond from Andrew Howroyd, Oct 01 2019

A285013 Number of periodic palindromic structures of length n using an infinite alphabet.

Original entry on oeis.org

1, 1, 2, 2, 5, 5, 13, 15, 41, 52, 144, 203, 578, 877, 2605, 4140, 12869, 21147, 69178, 115975, 398766, 678570, 2450406, 4213597, 15939952, 27644437, 109304914, 190899322, 787016238, 1382958545, 5931824093, 10480142147, 46673259309, 82864869804, 382473282504
Offset: 0

Views

Author

Andrew Howroyd, Apr 07 2017

Keywords

Comments

See A285012 for additional information. Permuting the symbols will not change the structure.

Links

Crossrefs

Row sums of A285012.
Cf. A165137, A284841, A285042.

Programs

  • PARI
    \\ Requires T from A285012.
seq(n)={my(A=T(n)); concat([1], vector(n, i, vecsum(A[i,])))} \\ Andrew Howroyd, Oct 02 2019

Extensions

a(0)=1 prepended and terms a(28) and beyond from Andrew Howroyd, Oct 02 2019
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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