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A113950
Number of n-fold 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
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.
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
Sequence in context: A122753 A016714 A211799 * A269944 A121906 A028360
KEYWORD
nonn,tabl
AUTHOR
Valery A. Liskovets, Nov 10 2005
STATUS
approved