%I #6 Dec 12 2014 20:56:06
%S 512,1728,1728,5832,7776,5832,19683,34992,34992,19683,46656,157464,
%T 209952,157464,46656,110592,466560,1259712,1259712,466560,110592,
%U 262144,1382400,4665600,10077696,4665600,1382400,262144,512000,4096000,17280000
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with nondecreasing sum of every three consecutive values in every row and column
%C Table starts
%C .....512.....1728.......5832.......19683........46656........110592
%C ....1728.....7776......34992......157464.......466560.......1382400
%C ....5832....34992.....209952.....1259712......4665600......17280000
%C ...19683...157464....1259712....10077696.....46656000.....216000000
%C ...46656...466560....4665600....46656000....259200000....1440000000
%C ..110592..1382400...17280000...216000000...1440000000....9600000000
%C ..262144..4096000...64000000..1000000000...8000000000...64000000000
%C ..512000..9600000..180000000..3375000000..31500000000..294000000000
%C .1000000.22500000..506250000.11390625000.124031250000.1350562500000
%C .1953125.52734375.1423828125.38443359375.488373046875.6204146484375
%H R. H. Hardin, <a href="/A251192/b251192.txt">Table of n, a(n) for n = 1..794</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 26; also a polynomial of degree 9 plus a quasipolynomial of degree 7 with period 3]
%F k=2: [order 35; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 3]
%F k=3: [order 44; also a polynomial of degree 15 plus a quasipolynomial of degree 13 with period 3]
%F k=4: [order 53; also a polynomial of degree 18 plus a quasipolynomial of degree 16 with period 3]
%F k=5: [order 62; also a polynomial of degree 21 plus a quasipolynomial of degree 19 with period 3]
%e Some solutions for n=2 k=4
%e ..0..0..0..1..1..1....0..0..0..1..1..1....0..0..0..0..1..0....0..0..0..0..1..1
%e ..1..1..0..1..1..1....0..0..0..0..0..0....1..1..0..1..1..0....1..0..0..1..1..1
%e ..0..0..0..0..0..1....0..1..0..1..1..0....0..1..0..0..1..0....0..0..0..0..1..0
%e ..0..1..1..1..1..1....0..0..1..1..1..1....0..0..0..0..1..0....0..0..0..1..1..1
%Y Column 4 is A250594
%Y Column 7 is A250861
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014