A296541 - OEIS

%I #4 Dec 15 2017 08:49:42

%S 1,1,1,1,3,1,1,5,5,1,1,8,16,8,1,1,15,37,37,15,1,1,26,96,126,96,26,1,1,

%T 45,254,431,431,254,45,1,1,80,654,1554,2104,1554,654,80,1,1,140,1709,

%U 5601,10734,10734,5601,1709,140,1,1,245,4472,20036,53995,78660,53995,20036

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s.

%C Table starts

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

%C .1...3....5.....8......15.......26........45..........80..........140

%C .1...5...16....37......96......254.......654........1709.........4472

%C .1...8...37...126.....431.....1554......5601.......20036........71722

%C .1..15...96...431....2104....10734.....53995......270584......1360373

%C .1..26..254..1554...10734....78660....560942.....3987615.....28515358

%C .1..45..654..5601...53995...560942...5705431....57470370....581613058

%C .1..80.1709.20036..270584..3987615..57470370...820373528..11761387456

%C .1.140.4472.71722.1360373.28515358.581613058.11761387456.239372827502

%H R. H. Hardin, <a href="/A296541/b296541.txt">Table of n, a(n) for n = 1..312</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-3) +a(n-5)

%F k=3: [order 12]

%F k=4: [order 39]

%e Some solutions for n=6 k=4

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

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

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

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

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

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

%Y Column 2 is A193147(n+1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 15 2017