A304270 - OEIS

%I #4 May 09 2018 10:14:57

%S 1,2,2,3,1,3,5,3,3,5,8,5,6,5,8,13,7,10,10,7,13,21,13,19,21,19,13,21,

%T 34,23,37,50,50,37,23,34,55,37,67,116,146,116,67,37,55,89,63,124,259,

%U 404,404,259,124,63,89,144,109,235,601,1074,1246,1074,601,235,109,144,233

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

%C Table starts

%C ..1..2...3....5....8....13.....21......34......55.......89.......144.......233

%C ..2..1...3....5....7....13.....23......37......63......109.......183.......309

%C ..3..3...6...10...19....37.....67.....124.....235......436.......808......1513

%C ..5..5..10...21...50...116....259.....601....1397.....3196......7359.....17016

%C ..8..7..19...50..146...404...1074....2990....8316....22660.....62314....172244

%C .13.13..37..116..404..1246...3788...12342...39252...122156....388150...1234248

%C .21.23..67..259.1074..3788..13767...53839..201274...741275...2806825..10575217

%C .34.37.124..601.2990.12342..53839..252509.1118021..4901568..22174589..99427544

%C .55.63.235.1397.8316.39252.201274.1118021.5755625.29475545.156881417.822798993

%H R. H. Hardin, <a href="/A304270/b304270.txt">Table of n, a(n) for n = 1..1012</a>

%F Empirical for column k:

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

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

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

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

%F k=5: [order 9] for n>10

%F k=6: [order 12] for n>13

%F k=7: [order 24] for n>25

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A003229(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 09 2018