A300108 - OEIS

%I #4 Feb 25 2018 06:12:54

%S 0,1,1,1,4,1,2,18,18,2,3,52,57,52,3,5,174,226,226,174,5,8,604,861,

%T 1041,861,604,8,13,2048,3432,5526,5526,3432,2048,13,21,6948,13268,

%U 29439,59014,29439,13268,6948,21,34,23652,51790,150416,526613,526613,150416,51790

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1......1.......2.........3...........5............8.............13

%C ..1.....4.....18......52.......174.........604.........2048...........6948

%C ..1....18.....57.....226.......861........3432........13268..........51790

%C ..2....52....226....1041......5526.......29439.......150416.........781647

%C ..3...174....861....5526.....59014......526613......4330629.......39686493

%C ..5...604...3432...29439....526613.....7603542.....96369782.....1370857737

%C ..8..2048..13268..150416...4330629....96369782...1781758380....37174337571

%C .13..6948..51790..781647..39686493..1370857737..37174337571..1206489116900

%C .21.23652.202533.4082439.361139457.19722172824.798263732216.40745626588281

%H R. H. Hardin, <a href="/A300108/b300108.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 20] for n>21

%F k=4: [order 67] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A297945.

%Y Column 3 is A299460.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Feb 25 2018