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A298635 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero. 6

%I

%S 1,1,1,1,5,1,1,6,6,1,1,17,2,17,1,1,24,5,5,24,1,1,53,7,15,7,53,1,1,94,

%T 14,25,25,14,94,1,1,173,21,45,34,45,21,173,1,1,340,41,81,61,61,81,41,

%U 340,1,1,601,70,186,107,163,107,186,70,601,1,1,1178,129,382,234,246,246,234

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 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.....1.....1.....1......1......1.......1

%C .1...5..6..17..24...53...94..173..340...601..1178..2137...4056...7565...14086

%C .1...6..2...5...7...14...21...41...70...129...233...428....783...1445....2664

%C .1..17..5..15..25...45...81..186..382...832..1778..3817...8229..17739...38337

%C .1..24..7..25..34...61..107..234..433...961..2031..4286...9049..19572...42207

%C .1..53.14..45..61..163..246..566.1334..2879..6223.14320..33446..76557..175161

%C .1..94.21..81.107..246..462..991.1953..4272..9838.22598..52716.122648..291782

%C .1.173.41.186.234..566..991.2134.4366..9639.22287.50362.114429.263499..617118

%C .1.340.70.382.433.1334.1953.4366.7520.18205.39703.92437.205166.484401.1134968

%H R. H. Hardin, <a href="/A298635/b298635.txt">Table of n, a(n) for n = 1..419</a>

%F Empirical for column k:

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

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

%F k=3: [order 11] for n>13

%F k=4: [order 23] for n>29

%F k=5: [order 58] for n>64

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297980.

%Y Column 3 is A297981.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 23 2018

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)