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Search: id:A113950
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| A113950 |
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Number of n-fold branched coverings of the Klein bottle with r cyclic branch points (n,r>=1); array read by downward antidiagonals. |
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3
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| 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
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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The odd bisection of the first column is A113948.
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REFERENCES
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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.
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FORMULA
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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).
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EXAMPLE
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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 ...
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CROSSREFS
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Cf. A113948, A113949.
Sequence in context: A132022 A122753 A016714 this_sequence A121906 A028360 A010301
Adjacent sequences: A113947 A113948 A113949 this_sequence A113951 A113952 A113953
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KEYWORD
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nonn,tabl
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Nov 10 2005
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