A255101 - OEIS

%I #6 Apr 21 2021 12:00:59

%S 36,77,77,179,189,179,419,539,539,419,991,1475,1838,1475,991,2345,

%T 4075,6110,6110,4075,2345,5537,11573,20928,25413,20928,11573,5537,

%U 13105,32627,72639,106848,106848,72639,32627,13105,31063,91821,250704,454332,554091

%N T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with no 3 X 3 subblock diagonal sum 1 and no antidiagonal sum 1 and no row sum 1 and no column sum 1.

%C Table starts

%C ....36.....77......179.......419........991........2345.........5537

%C ....77....189......539......1475.......4075.......11573........32627

%C ...179....539.....1838......6110......20928.......72639.......250704

%C ...419...1475.....6110.....25413.....106848......454332......1933924

%C ...991...4075....20928....106848.....554091.....2926453.....15422602

%C ..2345..11573....72639....454332....2926453....19198366....125525340

%C ..5537..32627...250704...1933924...15422602...125525340...1018478173

%C .13105..91821...868395...8248373...81332263...822095802...8275662960

%C .31063.259851..3018347..35227773..430226255..5400253601..67453730450

%C .73591.734851.10479598.150417081.2275433973.35458215276.549630067102

%H R. H. Hardin, <a href="/A255101/b255101.txt">Table of n, a(n) for n = 1..419</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 11] for n > 12;

%F k=2: [order 14];

%F k=3: [order 29] for n > 31;

%F k=4: [order 46] for n > 50;

%F k=5: [order 83] for n > 88.

%e Some solutions for n=4, k=4

%e ..1..0..1..1..1..1....0..1..1..0..1..1....1..1..1..1..1..0....1..1..1..1..0..1

%e ..1..1..1..0..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..0..1..1..1..0

%e ..0..1..1..1..1..1....1..1..1..1..0..1....1..1..1..1..1..1....1..1..1..1..1..1

%e ..1..1..1..1..1..1....1..1..1..1..1..1....1..0..1..1..1..1....1..1..1..1..1..1

%e ..1..0..1..1..1..1....0..1..1..1..1..1....1..1..1..1..1..0....1..1..1..1..1..1

%e ..1..1..1..1..1..0....1..1..0..1..1..0....1..1..0..1..1..1....1..1..1..1..0..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 14 2015