A297519 - OEIS

%I #4 Dec 31 2017 09:54:20

%S 1,2,1,3,5,1,4,17,11,1,6,33,49,24,1,9,65,128,177,55,1,13,193,363,624,

%T 727,123,1,19,529,1408,2610,3383,2445,276,1,28,1185,5079,15896,19187,

%U 16173,8931,621,1,41,2737,16104,85843,193087,134123,80436,33841,1395,1,60,7169

%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.

%C Table starts

%C .1....2......3.......4........6..........9...........13............19

%C .1....5.....17......33.......65........193..........529..........1185

%C .1...11.....49.....128......363.......1408.........5079.........16104

%C .1...24....177.....624.....2610......15896........85843........402072

%C .1...55....727....3383....19187.....193087......1671315......11283382

%C .1..123...2445...16173...134123....1995817.....25184119.....253060180

%C .1..276...8931...80436...956810...22251457....424461759....6257746155

%C .1..621..33841..406779..6834267..249462938...7287075949..156485261895

%C .1.1395.120079.2013490.48617437.2728125667.119542912709.3789277002360

%H R. H. Hardin, <a href="/A297519/b297519.txt">Table of n, a(n) for n = 1..241</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) +2*a(n-3) -a(n-5)

%F k=3: a(n) = a(n-1) +2*a(n-2) +30*a(n-3) +6*a(n-5) -124*a(n-6) -8*a(n-8) +64*a(n-9)

%F k=4: [order 32]

%F k=5: [order 54]

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-3)

%F n=2: a(n) = a(n-1) +4*a(n-3) +12*a(n-4)

%F n=3: [order 12]

%F n=4: [order 31]

%F n=5: [order 87]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A295091.

%Y Row 1 is A000930(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 31 2017