A318430 - OEIS

%I #4 Aug 26 2018 11:24:37

%S 0,1,1,1,5,1,2,16,16,2,3,50,36,50,3,5,160,147,147,160,5,8,511,417,889,

%T 417,511,8,13,1634,1353,3999,3999,1353,1634,13,21,5226,4095,20016,

%U 19645,20016,4095,5226,21,34,16716,12853,95349,132039,132039,95349,12853,16716

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

%C Table starts

%C ..0.....1.....1.......2........3.........5...........8...........13

%C ..1.....5....16......50......160.......511........1634.........5226

%C ..1....16....36.....147......417......1353........4095........12853

%C ..2....50...147.....889.....3999.....20016.......95349.......461349

%C ..3...160...417....3999....19645....132039......774731......4831925

%C ..5...511..1353...20016...132039...1216538.....9600648.....81327718

%C ..8..1634..4095...95349...774731...9600648....99435165...1103814944

%C .13..5226.12853..461349..4831925..81327718..1103814944..16560787736

%C .21.16716.39489.2221254.29346956.665822482.11993654843.238281611555

%H R. H. Hardin, <a href="/A318430/b318430.txt">Table of n, a(n) for n = 1..263</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)

%F k=3: [order 17] for n>20

%F k=4: [order 53] for n>59

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A317817.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 26 2018