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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}.
0
1, 2, 6, 24, 128, 928, 9280, 129152, 2515200, 68780544, 2647000064, 143580989440, 10988411686912, 1187350176604160, 181232621966082048, 39089521693818912768, 11916533065969825808384, 5135497592471003032846336, 3128995097443083790244380672, 2695613904312277811648715554816
OFFSET
1,2
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 {++-,+--}.
FORMULA
a(n) = 1 + Sum_{k=1..n-1} (2^k-1)*2^((n-1-k)*k).
MAPLE
seq(1 + add((2^k-1)*2^((n-1-k)*k), k=1..n-1), n=1..20); # Georg Fischer_, May 28 2024
PROG
(Python) def f(n): return 1+sum((2**k-1)*2**((n-1-k)*k) for k in range(1, n))
CROSSREFS
Cf. A048194.
Sequence in context: A201158 A356634 A191343 * A052862 A277211 A374153
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(20), a(21) joined by Georg Fischer, May 28 2024
STATUS
approved