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

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

1,2

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]

Links

Table of n, a(n) for n=1..28.

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

Crossrefs

Cf. A056411, A288627.

Sequence in context: A049297 A285664 A056391 * A089878 A057545 A015628

Adjacent sequences: A056427 A056428 A056429 * A056431 A056432 A056433

Keyword

nonn

Author

Marks R. Nester

Status

approved