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A300146 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 0,1,1,0,4,0,1,4,4,1,0,16,1,16,0,1,48,18,18,48,1,0,88,41,246,41,88,0,

%T 1,240,130,1043,1043,130,240,1,0,704,510,5368,13182,5368,510,704,0,1,

%U 1600,1740,37739,78147,78147,37739,1740,1600,1,0,4032,5554,219689,913701

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0....1....0.......1........0..........1............0..............1

%C .1....4....4......16.......48.........88..........240............704

%C .0....4....1......18.......41........130..........510...........1740

%C .1...16...18.....246.....1043.......5368........37739.........219689

%C .0...48...41....1043....13182......78147.......913701.......11122233

%C .1...88..130....5368....78147....1048462.....21602016......399714825

%C .0..240..510...37739...913701...21602016....783899343....25183985328

%C .1..704.1740..219689.11122233..399714825..25183985328..1507189100633

%C .0.1600.5554.1245482.99027295.6588098950.731705422933.74614900420199

%H R. H. Hardin, <a href="/A300146/b300146.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

%F k=3: [order 15] for n>17

%F k=4: [order 40] for n>42

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A298448.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Feb 26 2018

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Last modified May 26 10:17 EDT 2022. Contains 354086 sequences. (Running on oeis4.)