A300350 - OEIS

%I #4 Mar 03 2018 08:32:44

%S 0,1,1,1,2,1,2,6,6,2,3,15,9,15,3,5,37,26,26,37,5,8,90,57,58,57,90,8,

%T 13,223,133,152,152,133,223,13,21,550,306,325,306,325,306,550,21,34,

%U 1355,709,729,729,729,729,709,1355,34,55,3341,1642,1609,1496,1371,1496,1609

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..0....1....1....2....3.....5.....8....13....21.....34.....55.....89.....144

%C ..1....2....6...15...37....90...223...550..1355...3341...8237..20307...50064

%C ..1....6....9...26...57...133...306...709..1642...3805...8811..20409...47276

%C ..2...15...26...58..152...325...729..1609..3577...7931..17605..39106...86859

%C ..3...37...57..152..306...729..1496..3223..6893..14847..31957..68842..148439

%C ..5...90..133..325..729..1371..3092..6068.12638..26306..55227.116124..244628

%C ..8..223..306..729.1496..3092..5451.12038.22852..46541..95132.196177..405629

%C .13..550..709.1609.3223..6068.12038.20316.44961..83436.167732.339040..690762

%C .21.1355.1642.3577.6893.12638.22852.44961.73826.165976.303634.606479.1218187

%H R. H. Hardin, <a href="/A300350/b300350.txt">Table of n, a(n) for n = 1..682</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-2) +3*a(n-3) +2*a(n-4) +a(n-5)

%F k=3: a(n) = 2*a(n-1) +a(n-2) -2*a(n-5) -2*a(n-6) -2*a(n-7) -a(n-8) for n>10

%F k=4: [order 13] for n>16

%F k=5: [order 15] for n>19

%F k=6: [order 17] for n>22

%F k=7: [order 19] for n>25

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 03 2018