A298560 - OEIS

%I #4 Jan 21 2018 08:05:38

%S 0,1,1,1,4,1,2,18,18,2,3,52,56,52,3,5,174,219,219,174,5,8,604,796,956,

%T 796,604,8,13,2048,3079,4304,4304,3079,2048,13,21,6948,11614,19843,

%U 24364,19843,11614,6948,21,34,23652,44076,90153,138774,138774,90153,44076

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1......1.......2........3.........5..........8..........13...........21

%C ..1.....4.....18......52......174.......604.......2048........6948........23652

%C ..1....18.....56.....219......796......3079......11614.......44076.......167210

%C ..2....52....219.....956.....4304.....19843......90153......411915......1883419

%C ..3...174....796....4304....24364....138774.....781071.....4432262.....25124403

%C ..5...604...3079...19843...138774....983554....6852589....48019258....337105690

%C ..8..2048..11614...90153...781071...6852589...58699120...506226692...4381689438

%C .13..6948..44076..411915..4432262..48019258..506226692..5376664548..57373679100

%C .21.23652.167210.1883419.25124403.337105690.4381689438.57373679100.755503324152

%H R. H. Hardin, <a href="/A298560/b298560.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

%F k=3: [order 20] for n>21

%F k=4: [order 67] for n>70

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A297945.

%Y Column 3 is A297946.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 21 2018