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A367448
Number of chordal graphs on n vertices with a fixed perfect elimination ordering (e.g., 1,2,3,...,n)
0
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 -++.
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Jan 06 2024
STATUS
approved