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 A299521 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 1,1,1,1,1,1,1,1,1,1,1,2,12,2,1,1,5,5,5,5,1,1,9,33,8,33,9,1,1,22,55,

%T 41,41,55,22,1,1,45,132,117,285,117,132,45,1,1,101,272,476,1540,1540,

%U 476,272,101,1,1,218,630,1743,5869,12411,5869,1743,630,218,1,1,477,1355,7078

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

%C Table starts

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

%C .1...1...1....2......5.......9........22.........45..........101...........218

%C .1...1..12....5.....33......55.......132........272..........630..........1355

%C .1...2...5....8.....41.....117.......476.......1743.........7078.........28743

%C .1...5..33...41....285....1540......5869......31464.......164344........875093

%C .1...9..55..117...1540...12411.....89125.....826509......7492106......69199615

%C .1..22.132..476...5869...89125....902141...12982595....174024827....2513147146

%C .1..45.272.1743..31464..826509..12982595..310347496...6868847887..161346598727

%C .1.101.630.7078.164344.7492106.174024827.6868847887.249358437986.9535286392860

%H R. H. Hardin, <a href="/A299521/b299521.txt">Table of n, a(n) for n = 1..197</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 12] for n>13

%F k=4: [order 34] for n>36

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Feb 11 2018

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Last modified March 25 15:48 EDT 2023. Contains 361528 sequences. (Running on oeis4.)