A306129 - OEIS

%I #4 Jun 22 2018 07:36:49

%S 1,2,2,3,5,3,5,7,7,5,8,17,9,17,8,13,35,19,19,35,13,21,61,39,70,39,61,

%T 21,34,127,73,134,134,73,127,34,55,265,147,360,517,360,147,265,55,89,

%U 507,319,964,1351,1351,964,319,507,89,144,1013,681,2805,4441,4872,4441,2805

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ..2...5...7...17....35.....61.....127......265.......507........1013

%C ..3...7...9...19....39.....73.....147......319.......681........1451

%C ..5..17..19...70...134....360.....964.....2805......8207.......24747

%C ..8..35..39..134...517...1351....4441....18054.....66405......254943

%C .13..61..73..360..1351...4872...21926...106322....512165.....2629638

%C .21.127.147..964..4441..21926..143839...968676...6409145....45379428

%C .34.265.319.2805.18054.106322..968676..8721531..76600969...727128235

%C .55.507.681.8207.66405.512165.6409145.76600969.902758342.11497305073

%H R. H. Hardin, <a href="/A306129/b306129.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 13]

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

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303802.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 22 2018