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A303961 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 king-move adjacent elements, with upper left element zero. 7

%I #4 May 03 2018 12:47:28

%S 1,2,2,4,4,4,8,5,5,8,16,9,11,9,16,32,22,22,22,22,32,64,45,49,61,49,45,

%T 64,128,101,119,159,159,119,101,128,256,218,287,452,480,452,287,218,

%U 256,512,477,664,1228,1431,1431,1228,664,477,512,1024,1041,1563,3334,4137,4645

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

%C Table starts

%C ...1...2....4....8....16.....32.....64.....128......256......512......1024

%C ...2...4....5....9....22.....45....101.....218......477.....1041......2270

%C ...4...5...11...22....49....119....287.....664.....1563.....3716......8788

%C ...8...9...22...61...159....452...1228....3334.....9109....24981.....68361

%C ..16..22...49..159...480...1431...4137...12066....35589...104863....307928

%C ..32..45..119..452..1431...4645..14067...44800...144844...468709...1496959

%C ..64.101..287.1228..4137..14067..44492..156214...557417..1956218...6716752

%C .128.218..664.3334.12066..44800.156214..702361..2966679.11999856..46586544

%C .256.477.1563.9109.35589.144844.557417.2966679.14109468.62556978.267420497

%H R. H. Hardin, <a href="/A303961/b303961.txt">Table of n, a(n) for n = 1..577</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +2*a(n-4) -2*a(n-5) -6*a(n-6) -4*a(n-7) for n>8

%F k=4: [order 13] for n>17

%F k=5: [order 15] for n>21

%F k=6: [order 32] for n>38

%F k=7: [order 65] for n>71

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A052962 for n>2.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 03 2018

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Last modified June 21 09:23 EDT 2024. Contains 373542 sequences. (Running on oeis4.)