A380241 Array read by antidiagonals: T(n,k) is the number of rooted (2k)-regular planar maps with n vertices, n >= 0, k >= 0.
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 9, 1, 1, 1, 14, 100, 54, 1, 1, 1, 42, 1225, 3000, 378, 1, 1, 1, 132, 15876, 171500, 110000, 2916, 1, 1, 1, 429, 213444, 10001880, 30012500, 4550000, 24057, 1, 1, 1, 1430, 2944656, 591666768, 7981500240, 5987493750, 204000000, 208494, 1, 1
Offset: 0
Examples
Array begins: ==================================================================== n\k | 0 1 2 3 4 5 ... ----+--------------------------------------------------------------- 0 | 1 1 1 1 1 1 ... 1 | 1 1 2 5 14 42 ... 2 | 1 1 9 100 1225 15876 ... 3 | 1 1 54 3000 171500 10001880 ... 4 | 1 1 378 110000 30012500 7981500240 ... 5 | 1 1 2916 4550000 5987493750 7304332956480 ... 6 | 1 1 24057 204000000 1302227368750 7310748066293952 ... 7 | 1 1 208494 9690000000 301107909375000 7794097754539041792 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)
- E. A. Bender and E. R. Canfield, The number of degree restricted rooted maps on the sphere, SIAM J. Discrete Math. 7 (1994) 9-15.
- Zhicheng Gao and Mizan Rahman, Enumeration of k-poles, Annals of Combinatorics 1 (1997), pp. 55-66.
- W. T. Tutte, A Census of Slicings, Canad. J. Math. 14 (1962), 708-722.
- W. T. Tutte, A Census of Planar Maps, Canad. J. Math. 15 (1963), 249-271.
Crossrefs
Programs
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PARI
T(n,k)=if(k==0, 1, 2*binomial(2*k-1,k)^n*(n*k)!/(n!*(n*k - n + 2)!))
Formula
T(n,k) = 2*binomial(2*k-1, k)^n*(n*k)!/(n!*(n*k - n + 2)!) for k > 0.
Comments