A103944 Number of rooted unicursal n-edge maps in the plane (planar with a distinguished outside face).

1, 10, 93, 836, 7355, 63750, 546553, 4646920, 39250935, 329789450, 2758868981, 22995369996, 191074697203, 1583463268366, 13092015636465, 108024564809744, 889730213085167, 7316434446188562, 60078376613838829, 492692533579612180

Offset

1,2

References

V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.

Formula

a(n)=n*binomial(2n, n)sum_{i=0..n-2} binomial(n-2, i)(1/(n+1+i)+n/(n+2+i)), for n>1.

Recurrence: (n-1)*a(n) = 3*(3*n-4)*a(n-1) - 6*(n-9)*a(n-2) - 8*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 8^n*sqrt(n)/(6*sqrt(Pi)). - Vaclav Kotesovec, Oct 17 2012

Mathematica

Flatten[{1, Table[n*Binomial[2n, n]*Sum[Binomial[n-2, k]*(1/(n+1+k)+n/(n+2+k)), {k, 0, n-2}], {n, 2, 20}]}] (* Vaclav Kotesovec, Oct 17 2012 *)

Crossrefs

Cf. A069720, A103945.

Sequence in context: A287829 A265242 A262173 * A190989 A224696 A099295

Adjacent sequences: A103941 A103942 A103943 * A103945 A103946 A103947

Keyword

easy,nonn

Author

Valery A. Liskovets, Mar 17 2005

Status

approved