OFFSET
0,2
COMMENTS
A diamond of size n X n contains (n^2 + (n-1)^2) = A001844(n-1) squares.
For n > 0, a(n) is the number of ways to place non-adjacent counters on the black squares of a 2n-1 X 2n-1 checker board. The checker board is such that the black squares are in the corners. - Andrew Howroyd, Jan 16 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..20
Eric Weisstein's World of Mathematics, Independent Vertex Set
EXAMPLE
From Andrew Howroyd, Jan 16 2020: (Start)
Case n=2: The grid consists of 5 squares as shown below.
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If a prince is placed on the central square then a prince cannot be placed on the other 4 squares, otherwise princes can be placed in any combination. The total number of non-attacking configurations is then 1 + 2^4 = 17, so a(2) = 17.
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Case n=3: The grid consists of 13 squares as shown below:
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The total number of non-attacking configurations of princes is 689 so a(3) = 689.
(End)
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Matti De Craene (Matti.DeCraene(AT)rug.ac.be), May 14 2000
EXTENSIONS
a(0)=1 prepended and terms a(5) and beyond from Andrew Howroyd, Jan 15 2020
STATUS
approved