A302820 - OEIS

%I #4 Apr 13 2018 13:24:00

%S 1,2,2,4,8,4,8,20,25,8,16,52,75,81,16,32,136,220,389,264,32,64,360,

%T 731,1494,1852,857,64,128,960,2419,6905,9050,8485,2785,128,256,2576,

%U 7900,34957,57684,51476,41247,9050,256,512,6944,25645,170262,455224,454733

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 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.....75......220.......731........2419.........7900..........25645

%C ...8....81....389.....1494......6905.......34957.......170262.........800847

%C ..16...264...1852.....9050.....57684......455224......3252934.......21373833

%C ..32...857...8485....51476....454733.....5520999.....58122740......535479917

%C ..64..2785..41247...317216...3825201....72576189...1135257814....14619284475

%C .128..9050.196946..1927184..32123578...960564532..22294687742...402121386052

%C .256.29407.931243.11448173.264639685.12417289008.427140472935.10807066934912

%H R. H. Hardin, <a href="/A302820/b302820.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 49] for n>51

%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 15] for n>16

%F n=4: [order 67] for n>68

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A240478.

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

%Y Row 2 is A302323.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 13 2018