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A301608 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

%I A301608 #4 Mar 24 2018 11:33:49
%S A301608 1,1,1,1,2,1,1,2,2,1,1,3,2,3,1,1,6,8,8,6,1,1,10,13,25,13,10,1,1,21,26,
%T A301608 65,65,26,21,1,1,42,55,226,330,226,55,42,1,1,86,154,755,1297,1297,755,
%U A301608 154,86,1,1,179,356,2539,6393,8888,6393,2539,356,179,1,1,370,884,8794,30904
%N A301608 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
%C A301608 Table starts
%C A301608 .1..1...1....1......1.......1........1..........1...........1............1
%C A301608 .1..2...2....3......6......10.......21.........42..........86..........179
%C A301608 .1..2...2....8.....13......26.......55........154.........356..........884
%C A301608 .1..3...8...25.....65.....226......755.......2539........8794........30539
%C A301608 .1..6..13...65....330....1297.....6393......30904......154041.......764894
%C A301608 .1.10..26..226...1297....8888....60841.....421168.....2940940.....20639456
%C A301608 .1.21..55..755...6393...60841...591585....5880829....58383932....585233819
%C A301608 .1.42.154.2539..30904..421168..5880829...83224304..1180228568..16849867573
%C A301608 .1.86.356.8794.154041.2940940.58383932.1180228568.23865691820.485485211198
%H A301608 R. H. Hardin, <a href="/A301608/b301608.txt">Table of n, a(n) for n = 1..219</a>
%F A301608 Empirical for column k:
%F A301608 k=1: a(n) = a(n-1)
%F A301608 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A301608 k=3: [order 18]
%F A301608 k=4: [order 66]
%e A301608 Some solutions for n=5 k=4
%e A301608 ..0..0..1..1. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..0..1..1
%e A301608 ..0..0..1..1. .1..1..0..1. .1..0..1..0. .0..1..0..0. .0..0..1..1
%e A301608 ..1..1..0..0. .1..0..1..1. .0..1..0..1. .0..0..1..0. .0..0..1..1
%e A301608 ..1..1..0..0. .1..1..1..0. .1..0..1..0. .1..0..0..0. .0..1..0..0
%e A301608 ..1..1..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..0..0
%Y A301608 Column 2 is A240513(n-2).
%K A301608 nonn,tabl
%O A301608 1,5
%A A301608 _R. H. Hardin_, Mar 24 2018