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A209593 T(n,k)=Number of n X n 0..k arrays with every element equal to a diagonal or antidiagonal reflection.

%I A209593 #8 Jul 22 2025 21:50:42
%S A209593 2,3,16,4,81,192,5,256,3645,9216,6,625,28672,1476225,663552,7,1296,
%T A209593 140625,51380224,996451875,191102976,8,2401,513216,791015625,
%U A209593 161128382464,6053445140625,82556485632,9,4096,1529437,7316407296
%N A209593 T(n,k)=Number of n X n 0..k arrays with every element equal to a diagonal or antidiagonal reflection.
%C A209593 Table starts
%C A209593 ......2.........3............4.............5...............6................7
%C A209593 .....16........81..........256...........625............1296.............2401
%C A209593 ....192......3645........28672........140625..........513216..........1529437
%C A209593 ...9216...1476225.....51380224.....791015625......7316407296......47738317081
%C A209593 .663552.996451875.161128382464.8009033203125.191221621088256.2767247026234327
%H A209593 R. H. Hardin, <a href="/A209593/b209593.txt">Table of n, a(n) for n = 1..210</a>
%F A209593 T(n,k) = (k+1) ^ (2n-(n modulo 2)) * ((k+1)*(2k+1)) ^ ((n*n-2n+(n modulo 2))/4)
%e A209593 Some solutions for n=3 k=3
%e A209593 ..2..0..1....1..0..1....0..0..3....0..2..1....1..2..3....0..1..2....2..2..0
%e A209593 ..3..1..0....0..1..0....2..1..0....2..3..2....2..3..0....1..3..2....1..0..2
%e A209593 ..0..3..3....1..0..1....1..2..3....3..2..3....2..0..2....2..2..2....1..1..3
%Y A209593 Row 2 is A000583(n+1)
%K A209593 nonn,tabl
%O A209593 1,1
%A A209593 _R. H. Hardin_ Mar 10 2012