login
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
7

%I #4 Jan 18 2018 08:10:27

%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,29,29,23,5,8,49,63,112,63,49,8,

%T 13,99,167,432,432,167,99,13,21,189,473,1915,2231,1915,473,189,21,34,

%U 383,1205,7556,13271,13271,7556,1205,383,34,55,777,3161,29657,81019,117184

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ..1...3....7.....13......23.......49.........99.........189...........383

%C ..1...7...15.....29......63......167........473........1205..........3161

%C ..2..13...29....112.....432.....1915.......7556.......29657........123601

%C ..3..23...63....432....2231....13271......81019......454822.......2647771

%C ..5..49..167...1915...13271...117184....1142217.....9792821......87882289

%C ..8..99..473...7556...81019..1142217...16510708...212408711....2962142231

%C .13.189.1205..29657..454822..9792821..212408711..4149393799...87858962506

%C .21.383.3161.123601.2647771.87882289.2962142231.87858962506.2858791588717

%H R. H. Hardin, <a href="/A298396/b298396.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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

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

%F k=4: [order 68] for n>71

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A297953.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 18 2018