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A299682 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7

%I #4 Feb 16 2018 07:36:39

%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,73,45,45,73,32,64,157,147,

%T 211,147,157,64,128,353,506,1477,1477,506,353,128,256,869,1561,7279,

%U 13369,7279,1561,869,256,512,1993,5017,35408,95471,95471,35408,5017,1993,512

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2.....4.......8.......16.........32...........64............128

%C ...2....7....13......29.......73........157..........353............869

%C ...4...13....20......45......147........506.........1561...........5017

%C ...8...29....45.....211.....1477.......7279........35408.........196107

%C ..16...73...147....1477....13369......95471.......757628........6503333

%C ..32..157...506....7279....95471....1247427.....16311888......226655504

%C ..64..353..1561...35408...757628...16311888....346275749.....7835688567

%C .128..869..5017..196107..6503333..226655504...7835688567...289785610230

%C .256.1993.16429.1040287.52948378.3113437608.174961291252.10547510714203

%H R. H. Hardin, <a href="/A299682/b299682.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6

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

%F k=4: [order 61] for n>64

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A298215.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 16 2018

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)