A296019 - OEIS

%I #4 Dec 02 2017 21:51:46

%S 1,2,2,3,7,3,4,13,13,4,6,28,30,28,6,9,69,91,91,69,9,13,149,280,366,

%T 280,149,13,19,330,785,1644,1644,785,330,19,28,755,2319,6545,10703,

%U 6545,2319,755,28,41,1681,6816,26865,58506,58506,26865,6816,1681,41,60,3756,19796

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

%C Table starts

%C ..1....2.....3......4........6.........9.........13...........19............28

%C ..2....7....13.....28.......69.......149........330..........755..........1681

%C ..3...13....30.....91......280.......785.......2319.........6816.........19796

%C ..4...28....91....366.....1644......6545......26865.......112345........461363

%C ..6...69...280...1644....10703.....58506.....341979......2028843......11696474

%C ..9..149...785...6545....58506....437195....3547681.....28921472.....229650211

%C .13..330..2319..26865...341979...3547681...40196846....459874052....5101988967

%C .19..755..6816.112345..2028843..28921472..459874052...7361110427..113693158171

%C .28.1681.19796.461363.11696474.229650211.5101988967.113693158171.2440444635515

%H R. H. Hardin, <a href="/A296019/b296019.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-3)

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

%F k=3: [order 10]

%F k=4: [order 21]

%F k=5: [order 55]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000930(n+1).

%Y Column 2 is A183435.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 02 2017