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A279741 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 14

%I

%S 0,0,0,2,2,0,2,6,8,0,5,14,35,26,0,8,26,106,168,80,0,15,48,286,736,766,

%T 240,0,26,84,746,2948,4940,3402,708,0,46,146,1887,11434,29140,32430,

%U 14827,2062,0,80,250,4700,42494,167904,281350,209558,63680,5944,0,139

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C .0.....0.......2........2..........5...........8............15..............26

%C .0.....2.......6.......14.........26..........48............84.............146

%C .0.....8......35......106........286.........746..........1887............4700

%C .0....26.....168......736.......2948.......11434.........42494..........154886

%C .0....80.....766.....4940......29140......167904........927615.........5029822

%C .0...240....3402....32430.....281350.....2407152......19743140.......158848594

%C .0...708...14827...209558....2672708....33954530.....413326300......4935790522

%C .0..2062...63680..1337624...25057618...472691878....8539248826....151323545378

%C .0..5944..270313..8453760..232453138..6511502806..174560480712...4589874672896

%C .0.16990.1136546.52990574.2137856646.88926626284.3537506044402.137999764109606

%H R. H. Hardin, <a href="/A279741/b279741.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

%F k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

%F k=3: a(n) = 10*a(n-1) -35*a(n-2) +54*a(n-3) -45*a(n-4) +20*a(n-5) -4*a(n-6) for n>7

%F k=4: [order 16] for n>17

%F k=5: [order 25] for n>26

%F k=6: [order 64] for n>65

%F Empirical for row n:

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

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

%F n=3: [order 16] for n>18

%F n=4: [order 45] for n>50

%e Some solutions for n=4 k=4

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

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

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

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

%Y Row 1 is A006367(n-1).

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Dec 18 2016

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)