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

1,2

Comments

a(n) is the number of sign mappings X:([n] choose 2) -> {+,-} such that for any ordered 3-tuple a<b<c we have X(ab)X(ac)X(bc) not equal to -++.

Links

Table of n, a(n) for n=1..20.

Prog

(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

Crossrefs

Cf. A048192.

Sequence in context: A300519 A103365 A145086 * A052443 A153744 A266422

Adjacent sequences: A367445 A367446 A367447 * A367449 A367450 A367451

Keyword

nonn

Author

Manfred Scheucher and Robert Lauff, Jan 05 2024

Extensions

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

Status

approved