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A295531 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s. 8

%I #4 Nov 23 2017 09:27:46

%S 1,2,2,4,10,4,7,29,29,7,12,87,147,87,12,21,280,774,774,280,21,37,876,

%T 4080,7071,4080,876,37,65,2735,21489,64189,64189,21489,2735,65,114,

%U 8583,113466,588529,1012315,588529,113466,8583,114,200,26900,598374,5400933

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

%C Table starts

%C ...1.....2.......4.........7..........12............21...............37

%C ...2....10......29........87.........280...........876.............2735

%C ...4....29.....147.......774........4080.........21489...........113466

%C ...7....87.....774......7071.......64189........588529..........5400933

%C ..12...280....4080.....64189.....1012315......16031147........253594307

%C ..21...876...21489....588529....16031147.....437241277......11938414614

%C ..37..2735..113466...5400933...253594307...11938414614.....563330031268

%C ..65..8583..598374..49414072..4003959566..325438086413...26515589323171

%C .114.26900.3155426.452274232.63279327977.8875686431050.1248681784524804

%H R. H. Hardin, <a href="/A295531/b295531.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -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 ..0..1..1..1. .1..1..0..1. .0..0..1..1. .1..1..1..0. .0..1..1..0

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

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

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

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

%Y Column 1 is A005251(n+2).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 23 2017

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)