A368761 Number of labeled split graphs on n vertices such that {1..k} is independent and {k+1..n} is a clique for some k in {0..n}.

1, 2, 6, 24, 128, 928, 9280, 129152, 2515200, 68780544, 2647000064, 143580989440, 10988411686912, 1187350176604160, 181232621966082048, 39089521693818912768, 11916533065969825808384, 5135497592471003032846336, 3128995097443083790244380672, 2695613904312277811648715554816

Offset: 1

Author

Robert Lauff and Manfred Scheucher, Jan 05 2024

Keywords

• nonn

Comments

Also the number of sign mappings X:([n] choose 2) -> {+,-} such that for any ordered 3-tuple abc we have X(ab)X(ac)X(bc) not in {++-,+--}.

Crossrefs

Cf. A048194.

Programs

Maple

seq(1 + add((2^k-1)*2^((n-1-k)*k),k=1..n-1),n=1..20); # Georg Fischer_, May 28 2024

Python

def f(n): return 1+sum((2**k-1)*2**((n-1-k)*k) for k in range(1,n))

Formula

a(n) = 1 + Sum_{k=1..n-1} (2^k-1)*2^((n-1-k)*k).

Extensions

a(20), a(21) joined by Georg Fischer, May 28 2024