A252389 - OEIS

%I #7 Dec 03 2018 11:52:48

%S 785,637,799,916,1305,1894,2310,3280,4791,5934,8451,12386,15413,21987,

%T 32274,40226,57424,84343,105186,150199,220662,275253,393087,577550,

%U 720494,1028976,1511895,1886150,2693755,3958042,4937877,7052203,10362138

%N Number of (5+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 3 5 6 or 7.

%H R. H. Hardin, <a href="/A252389/b252389.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-3) - 4*a(n-6) + a(n-9) for n>14.

%F Empirical g.f.: x*(785 + 637*x + 799*x^2 - 2224*x^3 - 1243*x^4 - 1302*x^5 + 1786*x^6 + 608*x^7 + 411*x^8 - 427*x^9 - 86*x^10 - x^11 + x^12 - 2*x^13) / ((1 - x)*(1 + x + x^2)*(1 - 3*x^3 + x^6)). - _Colin Barker_, Dec 03 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

%Y Row 5 of A252384.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2014