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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.

%I A371979 #13 Apr 14 2024 17:36:07
%S A371979 1,3,8,24,84,276,880,3063,10692,36257,121580,436847,1530534,5259906,
%T A371979 18389910,65748491,230935493,799429185,2860613606,10203350814,
%U A371979 35899202776,125660232367,453360413253,1614905346286,5688690345179,20241845359246,72805688610204
%N 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.
%H A371979 Alois P. Heinz, <a href="/A371979/b371979.txt">Table of n, a(n) for n = 0..1788</a>
%H A371979 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wazir_(chess)">Wazir (chess)</a>
%e A371979 a(3) = 24 = A371967(3,2):
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   | W . W | | W . . | | W . . | | W . . | | W . . | | W . . |
%e A371979   | . . . | | . W . | | . . W | | . . . | | . . . | | . . . |
%e A371979   | . . . | | . . . | | . . . | | W . . | | . W . | | . . W |
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   | . W . | | . W . | | . W . | | . W . | | . W . | | . . W |
%e A371979   | W . . | | . . W | | . . . | | . . . | | . . . | | W . . |
%e A371979   | . . . | | . . . | | W . . | | . W . | | . . W | | . . . |
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   | . . W | | . . W | | . . W | | . . W | | . . . | | . . . |
%e A371979   | . W . | | . . . | | . . . | | . . . | | W . W | | W . . |
%e A371979   | . . . | | W . . | | . W . | | . . W | | . . . | | . W . |
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
%e A371979   | . . . | | . . . | | . . . | | . . . | | . . . | | . . . |
%e A371979   | W . . | | . W . | | . W . | | . . W | | . . W | | . . . |
%e A371979   | . . W | | W . . | | . . W | | W . . | | . W . | | W . W |
%e A371979   +-------+ +-------+ +-------+ +-------+ +-------+ +-------+ .
%p A371979 b:= proc(n, l) option remember; `if`(n=0, 1,
%p A371979       add(`if`(Bits[And](j, l)>0, 0, expand(b(n-1, j)*
%p A371979       x^add(i, i=Bits[Split](j)))), j=[0, 1, 2, 4, 5]))
%p A371979     end:
%p A371979 a:= n-> max(coeffs(b(n, 0))):
%p A371979 seq(a(n), n=0..30);
%Y A371979 Row maxima of A371967.
%Y A371979 Cf. A371978.
%K A371979 nonn
%O A371979 0,2
%A A371979 _Alois P. Heinz_, Apr 14 2024