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A317565 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7

%I #4 Jul 31 2018 12:38:49

%S 1,2,2,4,8,4,8,32,32,8,16,128,228,128,16,32,512,1619,1619,512,32,64,

%T 2048,11510,20312,11510,2048,64,128,8192,81814,255788,255788,81814,

%U 8192,128,256,32768,581541,3218063,5721314,3218063,581541,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ...2......8.......32........128...........512............2048..............8192

%C ...4.....32......228.......1619.........11510...........81814............581541

%C ...8....128.....1619......20312........255788.........3218063..........40491721

%C ..16....512....11510.....255788.......5721314.......127754533........2853437287

%C ..32...2048....81814....3218063.....127754533......5059110002......200422637482

%C ..64...8192...581541...40491721....2853437287....200422637482....14085130453968

%C .128..32768..4133710..509501103...63734296219...7940287015341...989910863217269

%C .256.131072.29383111.6410860875.1423516915862.314559200160931.69566536617221409

%H R. H. Hardin, <a href="/A317565/b317565.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)

%F k=3: a(n) = 6*a(n-1) +11*a(n-2) -11*a(n-3) -72*a(n-4) -54*a(n-5) for n>6

%F k=4: [order 17] for n>18

%F k=5: [order 62] for n>63

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A004171(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 31 2018

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)