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A371979
Number of ways of placing k non-attacking wazirs on a 3 X n board, where k is chosen so as to maximize this number.
3
1, 3, 8, 24, 84, 276, 880, 3063, 10692, 36257, 121580, 436847, 1530534, 5259906, 18389910, 65748491, 230935493, 799429185, 2860613606, 10203350814, 35899202776, 125660232367, 453360413253, 1614905346286, 5688690345179, 20241845359246, 72805688610204
OFFSET
0,2
LINKS
Wikipedia, Wazir (chess)
EXAMPLE
a(3) = 24 = A371967(3,2):
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
| W . W | | W . . | | W . . | | W . . | | W . . | | W . . |
| . . . | | . W . | | . . W | | . . . | | . . . | | . . . |
| . . . | | . . . | | . . . | | W . . | | . W . | | . . W |
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
| . W . | | . W . | | . W . | | . W . | | . W . | | . . W |
| W . . | | . . W | | . . . | | . . . | | . . . | | W . . |
| . . . | | . . . | | W . . | | . W . | | . . W | | . . . |
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
| . . W | | . . W | | . . W | | . . W | | . . . | | . . . |
| . W . | | . . . | | . . . | | . . . | | W . W | | W . . |
| . . . | | W . . | | . W . | | . . W | | . . . | | . W . |
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+
| . . . | | . . . | | . . . | | . . . | | . . . | | . . . |
| W . . | | . W . | | . W . | | . . W | | . . W | | . . . |
| . . W | | W . . | | . . W | | W . . | | . W . | | W . W |
+-------+ +-------+ +-------+ +-------+ +-------+ +-------+ .
MAPLE
b:= proc(n, l) option remember; `if`(n=0, 1,
add(`if`(Bits[And](j, l)>0, 0, expand(b(n-1, j)*
x^add(i, i=Bits[Split](j)))), j=[0, 1, 2, 4, 5]))
end:
a:= n-> max(coeffs(b(n, 0))):
seq(a(n), n=0..30);
CROSSREFS
Row maxima of A371967.
Cf. A371978.
Sequence in context: A088966 A242985 A148787 * A125655 A134165 A071016
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 14 2024
STATUS
approved