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A298133 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero. 7

%I

%S 0,0,0,0,1,0,0,2,2,0,0,5,4,5,0,0,10,13,13,10,0,0,25,62,15,62,25,0,0,

%T 54,223,233,233,223,54,0,0,125,826,1055,2621,1055,826,125,0,0,282,

%U 3200,5782,21537,21537,5782,3200,282,0,0,641,12098,36225,175014,285084,175014

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0...0.....0......0........0.........0...........0.............0..............0

%C .0...1.....2......5.......10........25..........54...........125............282

%C .0...2.....4.....13.......62.......223.........826..........3200..........12098

%C .0...5....13.....15......233......1055........5782.........36225.........205348

%C .0..10....62....233.....2621.....21537......175014.......1557284.......13225388

%C .0..25...223...1055....21537....285084.....3752401......52922003......714854991

%C .0..54...826...5782...175014...3752401....76791444....1706951987....36185741209

%C .0.125..3200..36225..1557284..52922003..1706951987...58599163176..1933759163417

%C .0.282.12098.205348.13225388.714854991.36185741209.1933759163417.99650656591710

%H R. H. Hardin, <a href="/A298133/b298133.txt">Table of n, a(n) for n = 1..197</a>

%F Empirical for column k:

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

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

%F k=3: [order 18]

%F k=4: [order 53] for n>56

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297860.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 13 2018

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Last modified October 26 18:30 EDT 2021. Contains 348268 sequences. (Running on oeis4.)