A305097 - OEIS

%I #4 May 25 2018 08:29:00

%S 0,1,1,1,3,1,2,9,9,2,3,10,14,10,3,5,27,17,17,27,5,8,109,64,20,64,109,

%T 8,13,168,158,37,37,158,168,13,21,349,229,142,333,142,229,349,21,34,

%U 1229,630,295,1987,1987,295,630,1229,34,55,2490,1626,459,2220,7273,2220,459

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

%C Table starts

%C ..0....1....1....2.....3......5......8......13.......21........34.........55

%C ..1....3....9...10....27....109....168.....349.....1229......2490.......4767

%C ..1....9...14...17....64....158....229.....630.....1626......2950.......6627

%C ..2...10...17...20....37....142....295.....459.....1201......3140.......5679

%C ..3...27...64...37...333...1987...2220....6525....47093....101012.....198933

%C ..5..109..158..142..1987...7273..10652...64966...320192....708423....2636757

%C ..8..168..229..295..2220..10652..23368..101212...548208...1755533....6005884

%C .13..349..630..459..6525..64966.101212..566292..6089154..19700744...69543035

%C .21.1229.1626.1201.47093.320192.548208.6089154.64803044.208417821.1176560812

%H R. H. Hardin, <a href="/A305097/b305097.txt">Table of n, a(n) for n = 1..241</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) +a(n-2) +8*a(n-3) -16*a(n-5) for n>6

%F k=3: [order 16] for n>17

%F k=4: [order 71] for n>72

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 25 2018