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A203656 T(n,k)=1/25 the number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

%I A203656 #7 Jul 22 2025 17:25:33
%S A203656 9,81,81,729,1517,729,6561,28057,28057,6561,59049,519445,1116249,
%T A203656 519445,59049,531441,9616161,44577561,44577561,9616161,531441,4782969,
%U A203656 178019197,1780968921,3906948333,1780968921,178019197,4782969,43046721,3295578857
%N A203656 T(n,k)=1/25 the number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.
%C A203656 Table starts
%C A203656 ........9..........81.............729...............6561.................59049
%C A203656 .......81........1517...........28057.............519445...............9616161
%C A203656 ......729.......28057.........1116249...........44577561............1780968921
%C A203656 .....6561......519445........44577561.........3906948333..........343812029649
%C A203656 ....59049.....9616161......1780968921.......343812029649........67213191427593
%C A203656 ...531441...178019197.....71156938905.....30292030417413.....13192335511091073
%C A203656 ..4782969..3295578857...2843024036697...2669260624372937...2592476403527692089
%C A203656 .43046721.61009378085.113591039131161.235230466316286557.509649251749126118193
%H A203656 R. H. Hardin, <a href="/A203656/b203656.txt">Table of n, a(n) for n = 1..112</a>
%e A203656 Some solutions for n=4 k=3
%e A203656 ..1..1..1..0....2..4..1..4....3..1..1..3....3..0..4..4....0..3..4..0
%e A203656 ..4..1..2..1....2..2..4..4....4..3..1..1....2..3..0..4....3..2..3..4
%e A203656 ..0..4..1..4....1..2..2..4....3..1..0..1....4..2..3..0....2..2..2..3
%e A203656 ..3..0..4..3....3..1..2..2....1..1..1..0....0..4..2..3....4..2..4..2
%e A203656 ..4..3..0..4....2..3..1..2....4..1..1..1....0..0..4..2....2..4..3..4
%Y A203656 Column 1 is A001019
%K A203656 nonn,tabl
%O A203656 1,1
%A A203656 _R. H. Hardin_ Jan 04 2012