A302623 - OEIS

%I #4 Apr 10 2018 19:13:13

%S 1,2,2,4,8,4,8,17,25,8,16,37,25,81,16,32,78,45,71,264,32,64,169,79,

%T 130,191,857,64,128,361,146,251,367,498,2785,128,256,778,286,497,896,

%U 917,1321,9050,256,512,1673,563,1051,2229,2669,2533,3505,29407,512,1024,3605

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

%C Table starts

%C ...1.....2....4.....8....16.....32......64......128.......256........512

%C ...2.....8...17....37....78....169.....361......778......1673.......3605

%C ...4....25...25....45....79....146.....286......563......1114.......2222

%C ...8....81...71...130...251....497....1051.....2274......4999......10972

%C ..16...264..191...367...896...2229....5771....15303.....41564.....113363

%C ..32...857..498...917..2669...9015...30536...106951....390471....1418770

%C ..64..2785.1321..2533..8283..36510..159831...722300...3485735...16654024

%C .128..9050.3505..6871.25770.150072..851266..5004858..32283797..204853561

%C .256.29407.9240.18334.79047.606756.4471550.34111427.294788397.2490596189

%H R. H. Hardin, <a href="/A302623/b302623.txt">Table of n, a(n) for n = 1..449</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 9] for n>11

%F k=4: [order 8] for n>10

%F k=5: [order 15] for n>20

%F k=6: [order 21] for n>27

%F k=7: [order 35] for n>43

%F Empirical for row n:

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

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

%F n=3: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) for n>8

%F n=4: [order 8] for n>11

%F n=5: [order 16] for n>21

%F n=6: [order 29] for n>35

%F n=7: [order 51] for n>62

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A240478.

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

%Y Row 2 is A281470.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 10 2018