A113950 Number of n-fold branched coverings of the Klein bottle with r cyclic branch points (n,r>=1); array read by downward antidiagonals.

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

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), 388-398.

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^(h-2)*(2*720^m+(-1)^r*2*120^m+2*48^m+(-1)^r*36^m+6^r) for 7-sheeted coverings of the non-orientable surface of genus h>=1, where m=h+r-2).

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