A317815 - OEIS

%I #4 Aug 07 2018 22:00:14

%S 1,1,1,1,2,1,1,2,2,1,1,3,2,3,1,1,5,4,4,5,1,1,10,5,7,5,10,1,1,23,8,34,

%T 34,8,23,1,1,54,9,56,38,56,9,54,1,1,131,28,77,94,94,77,28,131,1,1,321,

%U 44,228,230,142,230,228,44,321,1,1,789,60,551,552,434,434,552,551,60,789,1

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

%C Table starts

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

%C .1...2..2...3....5...10....23....54....131....321.....789....1943.....4788

%C .1...2..2...4....5....8.....9....28.....44.....60.....118.....256......409

%C .1...3..4...7...34...56....77...228....551...1300....3171....6929....16038

%C .1...5..5..34...38...94...230...552...1397...3674....9184...23878....60774

%C .1..10..8..56...94..142...434..1071...2279...6087...15953...40210...104488

%C .1..23..9..77..230..434..1575..4232..10738..32307...97258..284543...844473

%C .1..54.28.228..552.1071..4232.13712..35752.110093..343180.1067786..3331483

%C .1.131.44.551.1397.2279.10738.35752.112854.377515.1253484.4165180.14146154

%H R. H. Hardin, <a href="/A317815/b317815.txt">Table of n, a(n) for n = 1..364</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) +a(n-3) -a(n-4) -a(n-5) -a(n-6)

%F k=3: [order 17] for n>19

%F k=4: [order 48] for n>52

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 07 2018