OFFSET
0,1
COMMENTS
The centered square numbers are given by A001844. The diagram for the n-th centered square number is the set of integer pairs (x,y) such that |x| + |y| <= n.
LINKS
Eric Weisstein's World of Mathematics, Centered Square Number.
FORMULA
EXAMPLE
For n=1 the a(1) = 12 inequivalent colorings are:
0 1 1 0 1 1
0 0 0, 0 0 0, 1 0 0, 1 0 1, 1 0 1, and 1 0 1,
0 0 0 0 0 1
along with
1 0 0 1 0 0
1 1 1, 1 1 1, 0 1 1, 0 1 0, 0 1 0, and 0 1 0.
1 1 1 1 1 0
For n = 2, the corresponding diagram has A001844(2) = 13 boxes and a(2) = 1236 inequivalent colorings. For instance, the following two colorings are considered equivalent, because one can be transformed to the other by a reflection.
+---+ +---+
| 1 | | 1 |
+---+---+---+ +---+---+---+
| 1 | 1 | | | 1 | | 1 |
+---+---+---+---+---+ +---+---+---+---+---+
| 1 | | | 1 | | | 1 | 1 | | | 1 |
+---+---+---+---+---+ +---+---+---+---+---+
| 1 | | | | | 1 | |
+---+---+---+ +---+---+---+
| 1 | | |
+---+ +---+
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Apr 21 2024
STATUS
approved