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A274895 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-1) or (-2,0) and new values introduced in order 0..2. 11

%I

%S 1,1,2,2,4,3,4,12,7,6,8,36,16,14,12,16,108,37,38,26,24,32,324,86,104,

%T 84,50,48,64,972,200,290,275,192,95,96,128,2916,465,815,913,753,436,

%U 181,192,256,8748,1081,2291,3064,3017,2049,990,345,384,512,26244,2513,6434,10337

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-1) or (-2,0) and new values introduced in order 0..2.

%C Table starts

%C ...1...1....2.....4......8......16.......32........64........128.........256

%C ...2...4...12....36....108.....324......972......2916.......8748.......26244

%C ...3...7...16....37.....86.....200......465......1081.......2513........5842

%C ...6..14...38...104....290.....815.....2291......6434......18065.......50729

%C ..12..26...84...275....913....3064....10337.....34921.....117975......398560

%C ..24..50..192...753...3017...12217....49697....202749.....828828.....3391310

%C ..48..95..436..2049...9863...48269...237807...1173787....5803040....28746995

%C ..96.181..990..5602..32539..191974..1143185...6843349...41072451...246859250

%C .192.345.2253.15305.107369..767905..5539989..40156061..292253909..2133745005

%C .384.657.5121.41866.354366.3065418.26833885.236220817.2086382703.18485204565

%H R. H. Hardin, <a href="/A274895/b274895.txt">Table of n, a(n) for n = 1..420</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +4*a(n-2) -6*a(n-4) -a(n-5) +4*a(n-6) -a(n-8) for n>10

%F k=4: [order 16] for n>18

%F k=5: [order 32] for n>34

%F k=6: [order 64] for n>66

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) for n>2

%F n=2: a(n) = 3*a(n-1) for n>2

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

%F n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>6

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

%F n=6: [order 13] for n>14

%F n=7: [order 21] for n>22

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A003945(n-2).

%Y Column 2 is A052535(n+1).

%Y Row 1 is A000079(n-2).

%Y Row 2 is A003946(n-1).

%Y Row 3 is A010912(n-1).

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Jul 10 2016

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Last modified July 24 15:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)