A367448 - OEIS

%I #27 Jan 06 2024 22:58:44

%S 1,2,7,39,324,3839,62973,1402792,41946319,1673580047,88922215948,

%T 6297931501377,596303138919753,75787556639822258,12991109500044250083,

%U 3018313885461813882295,955168488432838276254520,413639698066068492610331231,246197679553110860511406200613,202212713843977008653180874488520

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

%C 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 -++.

%o (PARI)

%o a(n)={

%o   local(M=Map(Mat([1, 1])));

%o   my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));

%o   my(proc(p,m)=for(k=0, poldegree(p), acc(p + x*(1 + x)^k, polcoef(p,k)*m)));

%o   for(r=1, n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], proc(src[i, 1], src[i, 2])));

%o   vecsum(Mat(M)[,2])

%o } \\ _Andrew Howroyd_, Jan 06 2024

%Y Cf. A048192.

%K nonn

%O 1,2

%A _Manfred Scheucher_ and _Robert Lauff_, Jan 05 2024

%E Terms a(12) and beyond from _Andrew Howroyd_, Jan 06 2024