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A304676 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero. 7

%I #4 May 16 2018 14:47:36

%S 1,1,1,1,4,1,1,7,7,1,1,13,13,13,1,1,26,23,23,26,1,1,49,45,56,45,49,1,

%T 1,99,131,199,199,131,99,1,1,194,337,598,897,598,337,194,1,1,387,883,

%U 1950,3525,3525,1950,883,387,1,1,773,2389,6588,15544,20932,15544,6588,2389

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 6 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...4....7....13.....26......49.......99.......194.........387..........773

%C .1...7...13....23.....45.....131......337.......883........2389.........6599

%C .1..13...23....56....199.....598.....1950......6588.......21871........72947

%C .1..26...45...199....897....3525....15544.....68896......310438......1387613

%C .1..49..131...598...3525...20932...122388....711362.....4369285.....26155072

%C .1..99..337..1950..15544..122388...930123...7208807....57718628....454436233

%C .1.194..883..6588..68896..711362..7208807..73484449...779364745...8098139458

%C .1.387.2389.21871.310438.4369285.57718628.779364745.11082127004.153249721883

%H R. H. Hardin, <a href="/A304676/b304676.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) -4*a(n-4) for n>5

%F k=3: [order 18] for n>19

%F k=4: [order 70] for n>71

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A304004.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 16 2018

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Last modified July 21 13:28 EDT 2024. Contains 374474 sequences. (Running on oeis4.)