A303040 - OEIS

%I #4 Apr 17 2018 13:23:44

%S 1,2,2,3,3,4,5,11,6,8,8,21,14,10,16,13,31,28,35,21,32,21,113,56,74,71,

%T 42,64,34,363,150,234,197,186,86,128,55,813,360,869,703,544,459,179,

%U 256,89,1751,828,2926,3069,2494,1686,1287,370,512,144,5001,1906,8500,11079

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1...2....3.....5......8......13.......21........34.........55..........89

%C ...2...3...11....21.....31.....113......363.......813.......1751........5001

%C ...4...6...14....28.....56.....150......360.......828.......1906........4628

%C ...8..10...35....74....234.....869.....2926......8500......27931.......96592

%C ..16..21...71...197....703....3069....11079.....39281.....147655......574771

%C ..32..42..186...544...2494...13597....59654....251705....1186522.....5869222

%C ..64..86..459..1686...9882...63254...345668...1853428...10924077....67726475

%C .128.179.1287..5252..38855..298328..2060154..13840842..103929273...827923879

%C .256.370.3490.16336.158630.1487003.13122422.112389422.1107624272.11716920536

%H R. H. Hardin, <a href="/A303040/b303040.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

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

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

%F k=3: [order 13] for n>16

%F k=4: [order 70]

%F Empirical for row n:

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

%F n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6

%F n=3: [order 11] for n>12

%F n=4: [order 61] for n>62

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A240513.

%Y Row 1 is A000045(n+1).

%Y Row 2 is A302310.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 17 2018