login
Number of (n+2)X(1+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 3 6 or 7
1

%I #5 Dec 16 2014 13:51:56

%S 943,856,976,1481,2079,3265,5676,10939,21842,45450,94429,201843,

%T 436593,950880,2077933,4556174,9995748,21960671,48283531,106217277,

%U 233735492,514456023,1132428018,2493020906,5488771613,12085003787,26609253669

%N Number of (n+2)X(1+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 3 6 or 7

%C Column 1 of A252295

%H R. H. Hardin, <a href="/A252294/b252294.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -3*a(n-4) -7*a(n-5) -3*a(n-6) -13*a(n-7) +10*a(n-8) +12*a(n-9) +20*a(n-10) +20*a(n-11) +18*a(n-12) +12*a(n-13) -58*a(n-14) -84*a(n-15) -26*a(n-16) +46*a(n-17) +62*a(n-18) +26*a(n-19) -28*a(n-20) -40*a(n-21) -16*a(n-22) +16*a(n-23) +24*a(n-24) +8*a(n-25) for n>30

%e Some solutions for n=4

%e ..2..2..1....3..1..0....1..1..2....3..1..1....1..2..2....3..3..3....0..2..2

%e ..1..3..1....1..0..3....2..1..1....2..0..3....3..3..2....3..3..3....1..3..1

%e ..1..0..3....1..3..1....1..2..2....0..3..1....0..0..1....3..3..3....3..0..1

%e ..3..2..0....2..2..1....2..2..1....2..2..0....2..1..1....2..3..3....0..1..3

%e ..0..3..2....2..0..2....1..1..2....2..0..3....2..3..3....3..3..3....2..3..0

%e ..1..0..3....0..2..2....2..1..1....1..2..2....0..1..0....3..3..3....3..0..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2014