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A300372 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I #6 Mar 12 2018 14:28:26

%S 0,0,0,0,1,0,0,1,1,0,0,1,0,1,0,0,3,3,3,3,0,0,2,3,3,3,2,0,0,6,8,4,4,8,

%T 6,0,0,6,16,22,32,22,16,6,0,0,11,32,39,92,92,39,32,11,0,0,16,70,102,

%U 270,366,270,102,70,16,0,0,22,135,298,1262,1592,1592,1262,298,135,22,0,0,37,293

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C .0..0..0...0....0.....0......0.......0........0.........0...........0

%C .0..1..1...1....3.....2......6.......6.......11........16..........22

%C .0..1..0...3....3.....8.....16......32.......70.......135.........293

%C .0..1..3...3....4....22.....39.....102......298.......833........2105

%C .0..3..3...4...32....92....270....1262.....3561.....13976.......48859

%C .0..2..8..22...92...366...1592....6925....36101....161645......762469

%C .0..6.16..39..270..1592..12042...75739...490425...3084820....19634393

%C .0..6.32.102.1262..6925..75739..729062..5841423..53750463...469053654

%C .0.11.70.298.3561.36101.490425.5841423.70536528.833035233.10021999204

%H R. H. Hardin, <a href="/A300372/b300372.txt">Table of n, a(n) for n = 1..263</a>

%F Empirical for column k:

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

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

%F k=3: [order 14]

%F k=4: [order 43] for n>45

%e All solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A062200(n-2).

%K nonn,tabl

%O 1,17

%A _R. H. Hardin_, Mar 04 2018

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)