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Search: id:A113949
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| A113949 |
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Number of n-fold branched coverings of the projective plane with r cyclic branch points (n,r>=1); array read by downward antidiagonals. |
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+0
3
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| 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 2, 5, 8, 1, 1, 0, 11, 0, 16, 0, 1, 2, 21, 128, 232, 64, 1, 1, 0, 43, 0, 5680, 0, 264, 0, 1, 2, 85, 3968, 132448, 581696, 144504, 1580, 1, 1, 0, 171, 0, 3189184, 0, 107174448, 0, 10648, 0, 1, 2, 341, 140288, 76426624, 8297164544
(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 second column is A113947.
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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)+(-1)^r*2*120^(r-1)+2*48^(r-1)+(-1)^r*36^(r-1)+6^r)/7 (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 1 ...
0 2 0 2 0 2 0 ...
1 3 5 11 21 43 85 ...
0 8 0 128 0 3968 0 ...
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CROSSREFS
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Cf. A113947, A113950.
Sequence in context: A055212 A028422 A064577 this_sequence A152434 A143810 A128589
Adjacent sequences: A113946 A113947 A113948 this_sequence A113950 A113951 A113952
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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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