A381726 Number of minimum connected dominating sets in the n X n black bishop graph.
1, 2, 1, 1, 2, 13, 83, 513, 4052, 41197, 462069, 5597201, 76094134, 1153902701, 18981358311, 336018968449, 6413439874792, 131386321421901, 2867812411156521, 66426533670738769, 1629082910078009770, 42175861619149917325, 1148999152027728530363, 32856688248674995989889
Offset: 1
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Eric Weisstein's World of Mathematics, Black Bishop Graph.
- Eric Weisstein's World of Mathematics, Connected Dominating Set.
Programs
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Mathematica
Join[{1, 2}, Table[Sum[(2 k - 1)^(n - 2 k - 1) (n - 2 k)^(2 (k - 1)), {k, Floor[(n - 1)/2]}], {n, 3, 20}]] (* Eric W. Weisstein, Mar 22 2025 *) -
PARI
\\ B(n,k) is A072590. B(n,k) = n^(k-1) * k^(n-1) a(n) = if(n <= 2, n, sum(k=1, (n-1)\2, B(n-2*k, 2*k-1))) \\ Andrew Howroyd, Mar 20 2025
Formula
a(n) = Sum_{k=1..floor((n-1)/2)} A072590(n-2*k, 2*k-1) for n >= 3. - Andrew Howroyd, Mar 20 2025
Extensions
a(10) onwards from Andrew Howroyd, Mar 20 2025