A318350 - OEIS

%I #4 Aug 24 2018 11:12:36

%S 1,2,2,3,3,3,5,4,4,5,8,7,6,7,8,13,11,13,13,11,13,21,18,21,14,21,18,21,

%T 34,30,41,29,29,41,30,34,55,49,71,55,62,55,71,49,55,89,81,130,106,136,

%U 136,106,130,81,89,144,134,237,220,279,345,279,220,237,134,144,233,221,439

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

%C Table starts

%C ..1..2...3...5....8...13....21.....34.....55......89.....144......233.......377

%C ..2..3...4...7...11...18....30.....49.....81.....134.....221......365.......603

%C ..3..4...6..13...21...41....71....130....237.....439.....802.....1483......2734

%C ..5..7..13..14...29...55...106....220....432.....885....1788.....3642......7416

%C ..8.11..21..29...62..136...279....624...1344....2941....6444....14202.....31437

%C .13.18..41..55..136..345...842...2167...5544...14244...36572....94381....243153

%C .21.30..71.106..279..842..2429...7451..22996...70762..218768...677035...2090867

%C .34.49.130.220..624.2167..7451..27666.102454..375150.1393359..5163458..19078931

%C .55.81.237.432.1344.5544.22996.102454.463096.2057916.9235301.41554051.186399590

%H R. H. Hardin, <a href="/A318350/b318350.txt">Table of n, a(n) for n = 1..510</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = a(n-1) +2*a(n-3) -a(n-6)

%F k=3: [order 19] for n>25

%F k=4: [order 37] for n>45

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+1).

%Y Column 2 is A317767.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 24 2018