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A113949 Number of n-fold branched coverings of the projective plane with r cyclic branch points (n,r>=1); array read by downward antidiagonals. +0
3
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)
OFFSET

1,5

COMMENT

The second column is A113947.

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)+(-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).

EXAMPLE

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 ...

CROSSREFS

Cf. A113947, A113950.

Sequence in context: A055212 A028422 A064577 this_sequence A128589 A130162 A133736

Adjacent sequences: A113946 A113947 A113948 this_sequence A113950 A113951 A113952

KEYWORD

nonn,tabl

AUTHOR

Valery A. Liskovets (liskov(AT)im.bas-net.by), Nov 10 2005

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.


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