A301400 - OEIS

%I #4 Mar 20 2018 11:02:21

%S 0,0,0,0,1,0,0,2,2,0,0,4,3,4,0,0,9,13,13,9,0,0,19,44,78,44,19,0,0,41,

%T 156,446,446,156,41,0,0,88,554,2619,4857,2619,554,88,0,0,189,1963,

%U 15538,49325,49325,15538,1963,189,0,0,406,6964,92338,521514,885003,521514

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

%C .0...1....2......4........9.........19...........41.............88

%C .0...2....3.....13.......44........156..........554...........1963

%C .0...4...13.....78......446.......2619........15538..........92338

%C .0...9...44....446.....4857......49325.......521514........5457161

%C .0..19..156...2619....49325.....885003.....16325745......299552320

%C .0..41..554..15538...521514...16325745....528025038....16971131642

%C .0..88.1963..92338..5457161..299552320..16971131642...956047339302

%C .0.189.6964.549096.57311190.5507220522.546618326745.53967719265287

%H R. H. Hardin, <a href="/A301400/b301400.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) = a(n-1) +2*a(n-2) +a(n-3)

%F k=3: [order 15]

%F k=4: [order 45]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A078039(n-2).

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Mar 20 2018