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A300472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A300472 #4 Mar 06 2018 11:40:58
%S A300472 1,2,2,4,8,4,8,29,29,8,16,108,160,108,16,32,401,925,925,401,32,64,
%T A300472 1490,5363,8608,5363,1490,64,128,5536,31106,80914,80914,31106,5536,
%U A300472 128,256,20569,180397,759100,1231578,759100,180397,20569,256,512,76424,1046223
%N A300472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A300472 Table starts
%C A300472 ...1.....2.......4.........8..........16............32..............64
%C A300472 ...2.....8......29.......108.........401..........1490............5536
%C A300472 ...4....29.....160.......925........5363.........31106..........180397
%C A300472 ...8...108.....925......8608.......80914........759100.........7121067
%C A300472 ..16...401....5363.....80914.....1231578......18735889.......284885784
%C A300472 ..32..1490...31106....759100....18735889.....462538206.....11408562672
%C A300472 ..64..5536..180397...7121067...284885784...11408562672....456303004550
%C A300472 .128.20569.1046223..66808673..4332278363..281433652906..18253046515989
%C A300472 .256.76424.6067629.626787854.65881928079.6942908646999.730219136878799
%H A300472 R. H. Hardin, <a href="/A300472/b300472.txt">Table of n, a(n) for n = 1..264</a>
%F A300472 Empirical for column k:
%F A300472 k=1: a(n) = 2*a(n-1)
%F A300472 k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
%F A300472 k=3: a(n) = 6*a(n-1) -a(n-2) -a(n-3) +a(n-4) -4*a(n-5) +a(n-6) -a(n-7)
%F A300472 k=4: [order 22]
%F A300472 k=5: [order 58] for n>59
%e A300472 Some solutions for n=5 k=4
%e A300472 ..0..0..1..0. .0..1..0..0. .0..0..1..0. .0..1..1..0. .0..1..0..0
%e A300472 ..1..0..1..1. .1..0..1..0. .0..1..0..0. .1..0..1..1. .0..0..1..1
%e A300472 ..1..0..1..1. .1..0..1..1. .0..0..1..1. .0..0..1..0. .1..1..0..0
%e A300472 ..1..0..0..0. .0..1..0..0. .1..1..0..1. .1..1..0..0. .0..1..0..1
%e A300472 ..0..1..1..0. .1..1..1..0. .0..0..1..1. .0..0..1..1. .0..0..1..0
%Y A300472 Column 1 is A000079(n-1).
%Y A300472 Column 2 is A220547.
%K A300472 nonn,tabl
%O A300472 1,2
%A A300472 _R. H. Hardin_, Mar 06 2018