A299097 - OEIS

%I #4 Feb 02 2018 08:23:20

%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,73,41,41,73,32,64,157,101,

%T 125,101,157,64,128,353,242,574,574,242,353,128,256,869,578,1847,2828,

%U 1847,578,869,256,512,1993,1385,6007,9624,9624,6007,1385,1993,512,1024,4557

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

%C Table starts

%C ...1....2....4.....8.....16......32........64........128.........256

%C ...2....7...13....29.....73.....157.......353........869........1993

%C ...4...13...20....41....101.....242.......578.......1385........3368

%C ...8...29...41...125....574....1847......6007......22330.......78424

%C ..16...73..101...574...2828....9624.....44936.....204059......865754

%C ..32..157..242..1847...9624...42012....255009....1414647.....7786685

%C ..64..353..578..6007..44936..255009...2170819...16528508...123272050

%C .128..869.1385.22330.204059.1414647..16528508..161247816..1570964262

%C .256.1993.3368.78424.865754.7786685.123272050.1570964262.20536604982

%H R. H. Hardin, <a href="/A299097/b299097.txt">Table of n, a(n) for n = 1..199</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 68] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A298215.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 02 2018