A302322 - OEIS

%I #4 Apr 05 2018 09:52:53

%S 1,2,2,4,8,4,8,20,25,8,16,52,65,81,16,32,136,177,281,264,32,64,360,

%T 519,953,1144,857,64,128,960,1528,3559,4525,4321,2785,128,256,2576,

%U 4509,14022,20686,19734,18093,9050,256,512,6944,13329,55727,104932,110035

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

%C Table starts

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

%C ...2.....8.....20......52......136.......360........960........2576

%C ...4....25.....65.....177......519......1528.......4509.......13329

%C ...8....81....281.....953.....3559.....14022......55727......218945

%C ..16...264...1144....4525....20686....104932.....529381.....2593409

%C ..32...857...4321...19734...110035....708572....4521584....27478634

%C ..64..2785..18093...96956...659949...5542827...45861206...349722102

%C .128..9050..72746..458537..3834162..41843808..444688101..4252740185

%C .256.29407.285199.2098489.21619209.305929316.4176914829.49936266116

%H R. H. Hardin, <a href="/A302322/b302322.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 14]

%F k=4: [order 48] for n>49

%F Empirical for row n:

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

%F n=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) for n>4

%F n=3: [order 14] for n>15

%F n=4: [order 57] for n>58

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A240478.

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 05 2018