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A216332 Number of horizontal and antidiagonal neighbor colorings of the even squares of an n X 2 array with new integer colors introduced in row major order. 5
1, 2, 3, 10, 27, 114, 409, 2066, 9089, 52922, 272947, 1788850, 10515147, 76282138, 501178937, 3974779402, 28773452321, 247083681522, 1949230218691, 17984917069018, 153281759047387, 1510073008031682, 13806215066685433 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Number of vertex covers and independent vertex sets of the n-1 X n-1 black bishops graph. Equivalently, the number of ways to place any number of non-attacking bishops on the black squares of an n-1 X n-1 board. - Andrew Howroyd, May 08 2017
LINKS
Eric Weisstein's World of Mathematics, Black Bishop Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover
EXAMPLE
Some solutions for n=5:
..0..x....0..x....0..x....0..x....0..x....0..x....0..x....0..x....0..x....0..x
..x..1....x..1....x..1....x..0....x..1....x..1....x..0....x..1....x..1....x..0
..0..x....2..x....2..x....1..x....2..x....2..x....1..x....2..x....0..x....1..x
..x..2....x..0....x..1....x..2....x..1....x..0....x..1....x..0....x..1....x..2
..3..x....3..x....3..x....0..x....2..x....1..x....0..x....2..x....0..x....3..x
There are 5 black squares on a 3 X 3 board. There is 1 way to place no non-attacking bishops, 5 ways to place 1 and 4 ways to place 2 so a(4)=1+5+4=10. - Andrew Howroyd, Jun 06 2017
MATHEMATICA
Table[Sum[Binomial[Ceiling[n/2], k] BellB[n - k], {k, 0, Ceiling[n/2]}], {n, 0, 20}] (* Eric W. Weisstein, Jun 25 2017 *)
CROSSREFS
Column 2 of A216338.
Row sums of A274105(n-1) for n>2.
Sequence in context: A264759 A323680 A171190 * A007029 A298083 A099435
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 04 2012
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)