A320409 - OEIS

%I #4 Oct 12 2018 12:40:58

%S 1,2,2,4,6,4,8,14,14,8,16,35,47,35,16,32,95,156,156,95,32,64,257,548,

%T 786,548,257,64,128,700,1970,3761,3761,1970,700,128,256,1907,7049,

%U 18725,27236,18725,7049,1907,256,512,5202,25364,92578,191615,191615,92578

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

%C Table starts

%C ...1....2.....4.......8.......16.........32..........64...........128

%C ...2....6....14......35.......95........257.........700..........1907

%C ...4...14....47.....156......548.......1970........7049.........25364

%C ...8...35...156.....786.....3761......18725.......92578........463045

%C ..16...95...548....3761....27236.....191615.....1353623.......9623424

%C ..32..257..1970...18725...191615....1957026....19677729.....199877194

%C ..64..700..7049...92578..1353623...19677729...282206549....4085687781

%C .128.1907.25364..463045..9623424..199877194..4085687781...84346447443

%C .256.5202.91307.2308299.68454701.2025592349.58997871413.1737667793009

%H R. H. Hardin, <a href="/A320409/b320409.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7)

%F k=3: [order 23] for n>25

%F k=4: [order 83] for n>85

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A318018.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Oct 12 2018