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

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

Offset

1,5

Comments

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.

Links

Table of n, a(n) for n=1..61.

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: A064577 A371729 A322435 * A318808 A349935 A257991

Adjacent sequences: A113946 A113947 A113948 * A113950 A113951 A113952

Keyword

nonn,tabl

Author

Valery A. Liskovets, Nov 10 2005

Status

approved