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 A301407 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I #4 Mar 20 2018 11:11:46

%S 1,2,2,4,8,4,8,32,32,8,16,128,252,128,16,32,512,1988,1988,512,32,64,

%T 2048,15680,31012,15680,2048,64,128,8192,123676,483600,483600,123676,

%U 8192,128,256,32768,975492,7541492,14905344,7541492,975492,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

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

%C ...4.....32......252........1988..........15680...........123676

%C ...8....128.....1988.......31012.........483600..........7541492

%C ..16....512....15680......483600.......14905344........459428416

%C ..32...2048...123676.....7541492......459428416......27990353344

%C ..64...8192...975492...117605364....14160945920....1705287652128

%C .128..32768..7694176..1833990416...436482419456..103893157740576

%C .256.131072.60687676.28600063044.13453684678656.6329599807409536

%H R. H. Hardin, <a href="/A301407/b301407.txt">Table of n, a(n) for n = 1..391</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) = 7*a(n-1) +7*a(n-2)

%F k=4: a(n) = 13*a(n-1) +40*a(n-2) +9*a(n-3) -29*a(n-4) +4*a(n-5)

%F k=5: [order 8] for n>9

%F k=6: [order 22] for n>23

%F k=7: [order 45] for n>47

%e Some solutions for n=5 k=4

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 20 2018

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Last modified August 9 21:21 EDT 2024. Contains 375044 sequences. (Running on oeis4.)