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A216078 Number of horizontal and antidiagonal neighbor colorings of the odd squares of an n X 2 array with new integer colors introduced in row major order. 5
1, 1, 3, 7, 27, 87, 409, 1657, 9089, 43833, 272947, 1515903, 10515147, 65766991, 501178937, 3473600465, 28773452321, 218310229201, 1949230218691, 16035686850327, 153281759047387, 1356791248984295, 13806215066685433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of vertex covers and independent vertex sets of the n-1 X n-1 white bishops graph. Equivalently, the number of ways to place any number of non-attacking bishops on the white squares of an n-1 X n-1 board. - Andrew Howroyd, May 08 2017

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

Eric Weisstein's World of Mathematics, Independent Vertex Set

Eric Weisstein's World of Mathematics, Vertex Cover

Eric Weisstein's World of Mathematics, White Bishop Graph

EXAMPLE

Some solutions for n = 5:

  x 0   x 0   x 0   x 0   x 0   x 0   x 0   x 0   x 0   x 0

  1 x   1 x   1 x   1 x   1 x   1 x   1 x   1 x   1 x   1 x

  x 2   x 0   x 0   x 2   x 0   x 1   x 1   x 2   x 2   x 1

  0 x   2 x   1 x   3 x   1 x   0 x   2 x   3 x   0 x   0 x

  x 3   x 1   x 2   x 2   x 0   x 1   x 1   x 1   x 2   x 0

There are 4 white squares on a 3 X 3 board. There is 1 way to place no non-attacking bishops, 4 ways to place 1 and 2 ways to place 2 so a(4) = 1 + 4 + 2 = 7. - Andrew Howroyd, Jun 06 2017

CROSSREFS

Column 2 of A216084.

Row sums of A274106(n-1).

Cf. A216332, A201862, A286423.

Sequence in context: A148745 A148746 A148747 * A148748 A148749 A098465

Adjacent sequences:  A216075 A216076 A216077 * A216079 A216080 A216081

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 01 2012

STATUS

approved

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Last modified October 27 18:02 EDT 2021. Contains 348287 sequences. (Running on oeis4.)