A006389
Number of unsensed planar maps with n edges and without faces of degree 1.
Original entry on oeis.org
1, 1, 2, 6, 18, 68, 313, 1592, 9187, 57451, 384450, 2703970, 19769311
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A379433
Number of rooted planar maps with n edges and without faces of degree 1.
Original entry on oeis.org
1, 1, 3, 16, 96, 624, 4304, 31056, 232128, 1784752, 14043312, 112648848, 918456608, 7593649392, 63546379152, 537427956688, 4587713701248, 39488179213872, 342414691125104, 2989022121125136, 26249475365186016, 231786459869636464, 2056950693208881744
Offset: 0
A380365
Number of sensed combinatorial maps with n edges and without faces of degree 1.
Original entry on oeis.org
1, 1, 3, 11, 50, 365, 3782, 47935, 718202, 12245679, 233541489, 4920828395, 113495838798, 2843930973805, 76932818058660, 2234631397864123, 69368177318863458, 2291843543825994905, 80296746074069588380, 2973657775519950500203, 116065360915389313936460
Offset: 0
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InvEulerT(v)={dirdiv(Vec(log(1+x*Ser(v)),-#v), vector(#v,n,1/n))}
b(k,r)={if(k%2, if(r%2, 0, my(j=r/2); k^j*(2*j)!/(j!*2^j)), sum(j=0, r\2, binomial(r, 2*j)*k^j*(2*j)!/(j!*2^j)))}
C(k,r)={sum(i=0, r, (-1)^i/i!/k^i)}
S(n,k)={sum(r=0, 2*n\k, if(k*r%2==0, x^(k*r/2)*b(k,r)*C(k,r)), O(x*x^n))}
seq(n)={concat([1], InvEulerT(Vec(-1 + prod(k=1, 2*n, S(n,k)))))}
A006392
Number of sensed planar maps with n edges and without faces of degree 1 or 2.
Original entry on oeis.org
1, 0, 1, 4, 9, 34, 161, 830, 4779, 29092, 184510, 1208178, 8116922
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A006396
Number of sensed planar maps with n edges and without faces or vertices of degree 1.
Original entry on oeis.org
1, 0, 1, 2, 4, 10, 36, 132, 616, 3060, 16207, 88990, 503816
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A006400
Number of sensed simple planar maps with n edges and without vertices of degree 1.
Original entry on oeis.org
1, 0, 0, 1, 1, 2, 5, 11, 33, 117, 431, 1755, 7485
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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