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A300465 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A300465 #4 Mar 06 2018 11:29:53
%S A300465 0,0,0,0,1,0,0,2,2,0,0,4,2,4,0,0,9,8,8,9,0,0,19,22,28,22,19,0,0,41,68,
%T A300465 142,142,68,41,0,0,88,212,540,1146,540,212,88,0,0,189,652,2585,7456,
%U A300465 7456,2585,652,189,0,0,406,2017,11343,55663,78195,55663,11343,2017,406,0,0
%N A300465 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A300465 Table starts
%C A300465 .0...0....0.....0.......0.........0..........0............0..............0
%C A300465 .0...1....2.....4.......9........19.........41...........88............189
%C A300465 .0...2....2.....8......22........68........212..........652...........2017
%C A300465 .0...4....8....28.....142.......540.......2585........11343..........51501
%C A300465 .0...9...22...142....1146......7456......55663.......400028........2906875
%C A300465 .0..19...68...540....7456.....78195.....935121.....10913850......127028268
%C A300465 .0..41..212..2585...55663....935121...17675111....330639367.....6123205255
%C A300465 .0..88..652.11343..400028..10913850..330639367...9829599051...293961266876
%C A300465 .0.189.2017.51501.2906875.127028268.6123205255.293961266876.14061129641181
%H A300465 R. H. Hardin, <a href="/A300465/b300465.txt">Table of n, a(n) for n = 1..220</a>
%F A300465 Empirical for column k:
%F A300465 k=1: a(n) = a(n-1)
%F A300465 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
%F A300465 k=3: [order 15]
%F A300465 k=4: [order 52] for n>54
%e A300465 Some solutions for n=5 k=4
%e A300465 ..0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0
%e A300465 ..0..1..0..0. .0..1..1..0. .0..0..1..1. .0..1..1..0. .0..1..0..0
%e A300465 ..1..1..1..1. .1..1..0..0. .1..1..0..0. .1..1..0..1. .1..1..1..1
%e A300465 ..1..0..1..1. .1..0..0..1. .1..0..0..1. .1..0..1..1. .0..0..0..1
%e A300465 ..0..0..1..1. .0..0..1..1. .1..1..1..1. .0..0..1..1. .0..0..1..1
%Y A300465 Column 2 is A078039(n-2).
%K A300465 nonn,tabl
%O A300465 1,8
%A A300465 _R. H. Hardin_, Mar 06 2018