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A280284 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 6

%I #4 Dec 30 2016 20:56:24

%S 0,0,0,1,4,1,2,46,46,2,8,384,996,384,8,28,2894,16860,16860,2894,28,94,

%T 20444,259040,592416,259040,20444,94,304,138944,3753846,18844474,

%U 18844474,3753846,138944,304,960,918744,52433492,566131860,1240628942

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ....0........0............1..............2...............8...............28

%C ....0........4...........46............384............2894............20444

%C ....1.......46..........996..........16860..........259040..........3753846

%C ....2......384........16860.........592416........18844474........566131860

%C ....8.....2894.......259040.......18844474......1240628942......77217209188

%C ...28....20444......3753846......566131860.....77217209188....9962925424456

%C ...94...138944.....52433492....16393550046...4633270354464.1239330073038612

%C ..304...918744....713549156...462579750172.270955366695864

%C ..960..5954690...9525564453.12805032188772

%C .2976.38005496.125290653912

%H R. H. Hardin, <a href="/A280284/b280284.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

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

%F k=2: [order 8]

%F k=3: [order 24] for n>25

%e Some solutions for n=3 k=4

%e ..0..1..0..2. .0..1..1..0. .0..0..1..2. .0..0..1..1. .0..1..2..0

%e ..2..0..1..2. .2..0..2..0. .2..1..2..2. .1..0..2..0. .2..2..0..1

%e ..2..0..0..1. .0..2..2..1. .0..2..1..1. .2..1..1..2. .0..1..0..0

%Y Column 2 is A279523.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 30 2016

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)