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 A295352 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 3 1s. 8

%I #4 Nov 20 2017 12:23:29

%S 2,3,3,5,8,5,8,20,20,8,13,51,76,51,13,21,132,299,299,132,21,34,341,

%T 1198,1877,1198,341,34,55,883,4775,11964,11964,4775,883,55,89,2293,

%U 19214,76688,123783,76688,19214,2293,89,144,5964,77650,499257,1290706,1290706

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 3 1s.

%C Table starts

%C ..2....3......5........8.........13...........21.............34..............55

%C ..3....8.....20.......51........132..........341............883............2293

%C ..5...20.....76......299.......1198.........4775..........19214...........77650

%C ..8...51....299.....1877......11964........76688.........499257.........3279206

%C .13..132...1198....11964.....123783......1290706.......13795489.......149583916

%C .21..341...4775....76688....1290706.....22091007......390440690......7029925681

%C .34..883..19214...499257...13795489....390440690....11500075769....345835713946

%C .55.2293..77650..3279206..149583916...7029925681...345835713946..17390584281932

%C .89.5964.314916.21697056.1639232052.128195710958.10540491064074.885995909117214

%H R. H. Hardin, <a href="/A295352/b295352.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

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

%F k=3: [order 18]

%F k=4: [order 45]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+2).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 20 2017

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Last modified May 24 21:03 EDT 2024. Contains 372781 sequences. (Running on oeis4.)