A299948 - OEIS

%I #4 Feb 22 2018 07:36:24

%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,69,27,27,69,32,64,137,47,75,

%T 47,137,64,128,301,83,191,191,83,301,128,256,705,137,401,644,401,137,

%U 705,256,512,1461,235,952,1604,1604,952,235,1461,512,1024,3193,412,2258,4924

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ...2....7..13...29....69....137.....301......705......1461.......3193

%C ...4...13..20...27....47.....83.....137......235.......412........709

%C ...8...29..27...75...191....401.....952.....2258......5275......13250

%C ..16...69..47..191...644...1604....4924....16163.....46665.....147161

%C ..32..137..83..401..1604...4604...19269....79664....307083....1300811

%C ..64..301.137..952..4924..19269..116051...642696...3313121...19431636

%C .128..705.235.2258.16163..79664..642696..5133698..34716313..275351726

%C .256.1461.412.5275.46665.307083.3313121.34716313.330723200.3594724687

%H R. H. Hardin, <a href="/A299948/b299948.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6

%F k=3: [order 17] for n>19

%F k=4: [order 67] for n>70

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A297883.

%Y Column 3 is A299182.

%Y Column 4 is A299183.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 22 2018