|
Search: id:A027610
|
|
|
| A027610 |
|
Number of chordal planar triangulations; also number of planar triangulations with maximal number of triangles; also number of graphs obtained from the tetrahedron by repeatedly inserting vertices of degree 3 into a triangular face; also number of uniquely 4-colorable planar graphs; also number of simplicial 3-clusters with n cells.
(Formerly M2688)
|
|
+0
18
|
|
| 1, 1, 1, 3, 7, 24, 93, 434, 2110, 11002, 58713, 321776, 1792133, 10131027, 57949430, 334970205, 1953890318, 11489753730, 68054102361, 405715557048, 2433003221232, 14668536954744, 88869466378593, 540834155878536, 3304961537938269
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
Also arises in enumeration of spectral isomers of alkane systems (see Cyvin et al.). - N. J. A. Sloane (njas(AT)research.att.com), Aug 15 2006
Chordal planar triangulations: take planar triangulations on n nodes, divide them into classes according to how many triangles they contain (all have 2n-4 triangular faces but may have additional triangles); count triangulations in class with most triangles.
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
L. W. Beineke and R. E. Pippert, Enumerating dissectable polyhedra by their automorphism groups, Canad. J. Math., 26 (1974), 50-67.
S. J. Cyvin et al., Enumeration of staggered conformers of alkanes: complete solution ..., J. Molec. Struct., 413 (1997), 237-239.
Hering, F.; Read, R. C.; Shephard, G. C.; The enumeration of stack polytopes and simplicial clusters, Discrete Math., 40 (1982), 203-217.
|
|
MAPLE
|
A001764 := proc(m) RETURN((3*m)!/(m!*(2*m+1)!)); end; # Gives A001764(m)
A047749 := proc(m) local x; if m mod 2 = 1 then x := (m-1)/2; RETURN((3*x+1)!/((x+1)!*(2*x+1)!)); fi; RETURN(A001764(m/2)); end; # Gives A047749(m)
A027610 := proc(n) local N; N := 0; N := N + A001764(n)/(12*(n+1)); if n mod 2 = 0 then N := N + 5/24*A001764(n/2); fi; if (n-1) mod 3 = 0 then N := N + 1/3*A001764((n-1)/3); fi; if (n-1) mod 4 = 0 then N := N + 1/4*A001764((n-1)/4); fi;
if (n-2) mod 6 = 0 then N := N + 1/6*A001764((n-2)/6); fi; N := N + 3/8*A047749(n); if (2*n-1) mod 3 = 0 then N := N + 1/6*A047749((2*n-1)/3); fi; RETURN(N); end;
|
|
CROSSREFS
|
Sum of A047776, A047775, A047774, A047773, A047762, A047760, A047758, A047754, A047753, A047752, A047751, A047771, A047769, A047766 (twice), A047765, A047764.
Sequence in context: A148720 A038169 A007172 this_sequence A135688 A005642 A019055
Adjacent sequences: A027607 A027608 A027609 this_sequence A027611 A027612 A027613
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
Gordon Royle (gordon(AT)maths.uwa.edu.au)
|
|
|
Search completed in 0.002 seconds
|
