

A113950


Number of nfold branched coverings of the Klein bottle with r cyclic branch points (n,r>=1); array read by downward antidiagonals.


2



1, 1, 0, 1, 4, 5, 1, 0, 13, 0, 1, 4, 23, 104, 44, 1, 0, 49, 0, 1256, 0, 1, 4, 95, 2720, 27344, 30608, 1266, 1, 0, 193, 0, 666656, 0, 1071540, 0, 1, 4, 383, 93824, 15911744, 415444544, 743214744
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OFFSET

1,5


COMMENTS

The odd bisection of the first column is A113948.


REFERENCES

J. H. Kwak, A. Mednykh and V. Liskovets, Enumeration of branched coverings of nonorientable surfaces with cyclic branch points, SIAM J. Discrete Math., Vol. 19, No. 2 (2005), 388398.


LINKS

Table of n, a(n) for n=1..43.


FORMULA

E.g. for n=7 and r>=1, a(7, r)=2*720^r+(1)^r*2*120^r+2*48^r+(1)^r*36^r+6^r (more generally, a(7, r, h)=7^(h2)*(2*720^m+(1)^r*2*120^m+2*48^m+(1)^r*36^m+6^r) for 7sheeted coverings of the nonorientable surface of genus h>=1, where m=h+r2).


EXAMPLE

The array begins:
1 1 1 1 1 1 ...
0 4 0 4 0 4 ...
5 13 23 49 95 193 ...
0 104 0 2720 0 93824 ...


CROSSREFS

Cf. A113948, A113949.
Sequence in context: A122753 A016714 A211799 * A269944 A121906 A028360
Adjacent sequences: A113947 A113948 A113949 * A113951 A113952 A113953


KEYWORD

nonn,tabl


AUTHOR

Valery A. Liskovets, Nov 10 2005


STATUS

approved



