%I #4 Dec 22 2014 09:16:42
%S 61,155,155,357,259,357,752,488,488,752,1808,369,1337,369,1808,4045,
%T 702,551,551,702,4045,8513,2301,2068,742,2068,2301,8513,19432,1864,
%U 6961,1625,1625,6961,1864,19432,42308,3971,2891,2795,3186,2795,2891,3971,42308
%N T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every consecutive three elements in every row and column not having exactly two distinct values, and in every diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order
%C Table starts
%C ....61...155...357...752..1808...4045..8513..19432..42308..88615.195983..419484
%C ...155...259...488...369...702...2301..1864...3971..13398..11033..23486...78603
%C ...357...488..1337...551..2068...6961..2891..10687..35835..15328..56023..186554
%C ...752...369...551...742..1625...2795..3763...8275..14320..19355..42636...73806
%C ..1808...702..2068..1625..3186...9869..7897..15217..46089..37348..72215..218508
%C ..4045..2301..6961..2795..9869..30949.13010..45797.138103..59021.201153..603059
%C ..8513..1864..2891..3763..7897..13010.17895..36732..58811..78891.160955..259629
%C .19432..3971.10687..8275.15217..45797.36732..69935.206185.164273.299025..854263
%C .42308.13398.35835.14320.46089.138103.58811.206185.626266.265685.899078.2570383
%C .88615.11033.15328.19355.37348..59021.78891.164273.265685.365400.722799.1111091
%H R. H. Hardin, <a href="/A252811/b252811.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 12] for n>14
%F k=2: [order 10] for n>16
%F k=3: [order 16] for n>19
%F k=4: a(n) = 6*a(n-3) -4*a(n-6) -2*a(n-9) +a(n-12) for n>15
%F k=5: [order 30] for n>34
%F k=6: [order 40] for n>46
%F k=7: [order 34] for n>39
%e Some solutions for n=2 k=4
%e ..0..1..2..0..3..4....0..1..2..0..1..2....0..1..2..0..3..2....0..1..2..0..3..2
%e ..0..2..1..0..4..1....1..1..1..1..1..1....2..2..2..2..2..2....3..0..2..3..0..2
%e ..0..0..0..0..0..0....2..1..0..2..1..0....3..0..2..1..4..2....2..2..2..2..2..2
%e ..0..1..4..0..1..3....3..1..2..0..1..3....0..3..2..4..1..2....4..3..2..0..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 22 2014