login
A113949
Number of n-fold branched coverings of the projective plane with r cyclic branch points (n,r>=1); array read by downward antidiagonals.
2
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.
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
Sequence in context: A064577 A371729 A322435 * A318808 A349935 A257991
KEYWORD
nonn,tabl
AUTHOR
Valery A. Liskovets, Nov 10 2005
STATUS
approved