

A054867


Number of nonattacking configurations on a diamond of size n, where a prince attacks the four adjacent nondiagonal squares.


3



1, 2, 17, 689, 139344, 142999897, 748437606081, 19999400591072512, 2728539172202554958697, 1900346273206544901717879089, 6755797872872106084596492075448192, 122584407857548123729431742141838309441329, 11352604691637658946858196503018301306800588837281
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OFFSET

0,2


COMMENTS

A diamond of size n X n contains (n^2 + (n1)^2) = A001844(n1) squares.
For n > 0, a(n) is the number of ways to place nonadjacent counters on the black squares of a 2n1 X 2n1 checker board. The checker board is such that the black squares are in the corners.  Andrew Howroyd, Jan 16 2020


LINKS



EXAMPLE

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 nonattacking configurations is then 1 + 2^4 = 17, so a(2) = 17.
.
Case n=3: The grid consists of 13 squares as shown below:
__
______
__________
__________
______
__
The total number of nonattacking 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



