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A296974 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 4 or 5 king-move neighboring 1s. 8

%I #4 Dec 22 2017 12:56:25

%S 1,1,1,1,5,1,1,11,11,1,1,21,31,21,1,1,59,78,78,59,1,1,145,295,274,295,

%T 145,1,1,323,959,1418,1418,959,323,1,1,793,2958,6573,13543,6573,2958,

%U 793,1,1,1939,9835,29590,101352,101352,29590,9835,1939,1,1,4561,32104,140427

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 4 or 5 king-move neighboring 1s.

%C Table starts

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

%C .1....5....11.....21.......59........145.........323...........793

%C .1...11....31.....78......295........959........2958..........9835

%C .1...21....78....274.....1418.......6573.......29590........140427

%C .1...59...295...1418....13543.....101352......711867.......5662206

%C .1..145...959...6573...101352....1154298....12662763.....158665988

%C .1..323..2958..29590...711867...12662763...222799447....4440619952

%C .1..793..9835.140427..5662206..158665988..4440619952..143300513381

%C .1.1939.32104.665654.44485796.1952861999.87137716095.4520161193750

%H R. H. Hardin, <a href="/A296974/b296974.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) -a(n-2) +6*a(n-3) -4*a(n-4) +2*a(n-5)

%F k=3: [order 17]

%F k=4: [order 48]

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 22 2017

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)