A305040 - OEIS

%I #4 May 24 2018 08:44:10

%S 1,2,2,4,4,4,8,3,3,8,16,5,7,5,16,32,8,7,7,8,32,64,13,13,19,13,13,64,

%T 128,21,23,26,26,23,21,128,256,34,37,61,43,61,37,34,256,512,55,63,143,

%U 109,109,143,63,55,512,1024,89,109,277,319,362,319,277,109,89,1024,2048,144

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1..2...4...8...16...32.....64....128.....256......512......1024.......2048

%C ...2..4...3...5....8...13.....21.....34......55.......89.......144........233

%C ...4..3...7...7...13...23.....37.....63.....109......183.......309........527

%C ...8..5...7..19...26...61....143....277.....568.....1244......2600.......5369

%C ..16..8..13..26...43..109....319....718....1632.....4351.....10773......25199

%C ..32.13..23..61..109..362...1359...3503....9721....31745.....92958.....264320

%C ..64.21..37.143..319.1359...7757..28535..104561...483316...2036051....7957330

%C .128.34..63.277..718.3503..28535.135992..601711..3666530..20376186..100132274

%C .256.55.109.568.1632.9721.104561.601711.3230419.25079880.172103176.1036410400

%H R. H. Hardin, <a href="/A305040/b305040.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) = a(n-1) +a(n-2) for n>4

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

%F k=4: a(n) = a(n-1) +5*a(n-3) +a(n-4) -4*a(n-6) -4*a(n-7) for n>11

%F k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) -14*a(n-6) -4*a(n-7) for n>11

%F k=6: [order 13] for n>19

%F k=7: [order 46] for n>51

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A000045(n+1) for n>2.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 24 2018