A367448 Number of chordal graphs on n vertices with a fixed perfect elimination ordering (e.g., 1,2,3,...,n).

1, 2, 7, 39, 324, 3839, 62973, 1402792, 41946319, 1673580047, 88922215948, 6297931501377, 596303138919753, 75787556639822258, 12991109500044250083, 3018313885461813882295, 955168488432838276254520, 413639698066068492610331231, 246197679553110860511406200613, 202212713843977008653180874488520

Offset: 1

Author

Manfred Scheucher and Robert Lauff, Jan 05 2024

Keywords

• nonn

Comments

a(n) is the number of sign mappings X:([n] choose 2) -> {+,-} such that for any ordered 3-tuple a

Crossrefs

Cf. A048192.

Programs

PARI

a(n)={
  local(M=Map(Mat([1, 1])));
  my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));
  my(proc(p,m)=for(k=0, poldegree(p), acc(p + x*(1 + x)^k, polcoef(p,k)*m)));
  for(r=1, n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], proc(src[i, 1], src[i, 2])));
  vecsum(Mat(M)[,2])
} \\ Andrew Howroyd, Jan 06 2024

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 06 2024

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