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

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

Author

Marks R. Nester

Keywords

• nonn

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