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A269035 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once. 13

%I

%S 0,3,0,12,24,0,36,48,120,0,96,216,348,504,0,240,672,2166,2136,1944,0,

%T 576,2208,9528,18384,12228,7128,0,1344,6912,44760,115656,146064,67104,

%U 25272,0,3072,21408,198816,785124,1326576,1114848,357756,87480,0,6912,65280

%N T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%C Table starts

%C .0......3.......12.........36...........96............240.............576

%C .0.....24.......48........216..........672...........2208............6912

%C .0....120......348.......2166.........9528..........44760..........198816

%C .0....504.....2136......18384.......115656.........785124.........4998648

%C .0...1944....12228.....146064......1326576.......13031664.......119790816

%C .0...7128....67104....1114848.....14710368......208867428......2783857776

%C .0..25272...357756....8277072....159397596.....3266423688.....63310818360

%C .0..87480..1867560...60218112...1698064656....50155587360...1416701634552

%C .0.297432..9593844..431354928..17853542544...759280601376..31304407671636

%C .0.997272.48665904.3052215072.185754411168.11364951702132.684763778434512

%H R. H. Hardin, <a href="/A269035/b269035.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

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

%F k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3

%F k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5

%F k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5

%F k=5: [order 12] for n>13

%F k=6: [order 18] for n>19

%F k=7: [order 38] for n>39

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -4*a(n-2)

%F n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)

%F n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8

%F n=4: [order 12] for n>14

%F n=5: [order 20] for n>22

%F n=6: [order 46] for n>48

%F n=7: [order 92] for n>94

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 2 is A268633.

%Y Row 1 is A167667(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 18 2016

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Last modified July 16 09:13 EDT 2020. Contains 335784 sequences. (Running on oeis4.)