A299321 - OEIS

%I #4 Feb 06 2018 13:49:23

%S 1,1,1,1,1,1,1,1,1,1,1,2,15,2,1,1,5,10,10,5,1,1,9,70,12,70,9,1,1,22,

%T 146,130,130,146,22,1,1,45,434,284,1306,284,434,45,1,1,101,1206,1557,

%U 6051,6051,1557,1206,101,1,1,218,3228,5838,38035,44381,38035,5838,3228,218,1

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .1...1....1.....1.......1........1..........1............1.............1

%C .1...1....1.....2.......5........9.........22...........45...........101

%C .1...1...15....10......70......146........434.........1206..........3228

%C .1...2...10....12.....130......284.......1557.........5838.........24821

%C .1...5...70...130....1306.....6051......38035.......234329.......1457212

%C .1...9..146...284....6051....44381.....473924......4898412......51303757

%C .1..22..434..1557...38035...473924....7885194....132676384....2249698337

%C .1..45.1206..5838..234329..4898412..132676384...3745566028..105240244212

%C .1.101.3228.24821.1457212.51303757.2249698337.105240244212.4909629881306

%H R. H. Hardin, <a href="/A299321/b299321.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>5

%F k=3: [order 10] for n>12

%F k=4: [order 29] for n>30

%e Some solutions for n=5 k=4

%e ..0..0..0..1. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..1..1..0

%e ..0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1

%e ..1..1..0..0. .0..1..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..1

%e ..1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..0..0

%e ..0..1..1..1. .0..1..1..1. .0..0..0..0. .1..0..0..1. .1..1..0..0

%Y Column 2 is A052962(n-2).

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Feb 06 2018