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A269011 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once. 13

%I #4 Feb 17 2016 12:04:50

%S 0,1,0,2,4,0,5,8,15,0,10,36,46,48,0,20,88,305,224,145,0,38,272,1078,

%T 2136,1066,420,0,71,696,4948,10976,14240,4952,1183,0,130,1900,18210,

%U 73568,109058,91048,22654,3264,0,235,4856,73277,390064,1049588,1053432,566656

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

%C Table starts

%C .0.....1.......2.........5.........10...........20.............38

%C .0.....4.......8........36.........88..........272............696

%C .0....15......46.......305.......1078.........4948..........18210

%C .0....48.....224......2136......10976........73568.........390064

%C .0...145....1066.....14240.....109058......1049588........8134304

%C .0...420....4952.....91048....1053432.....14382480......164351184

%C .0..1183...22654....566656...10002542....192100836.....3258530608

%C .0..3264..102416...3456320...93733440...2516546784....63679868768

%C .0..8865..458674..20760192..869397882..32481770852..1230707111424

%C .0.23780.2038328.123186784.7996744280.414339126768.23573013881888

%H R. H. Hardin, <a href="/A269011/b269011.txt">Table of n, a(n) for n = 1..721</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)

%F k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7

%F k=5: [order 12]

%F k=6: [order 14]

%F k=7: [order 24] for n>25

%F Empirical for row n:

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

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

%F n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)

%F n=4: [order 8]

%F n=5: [order 14]

%F n=6: [order 20]

%F n=7: [order 32]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 2 is A093967.

%Y Row 1 is A001629.

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Feb 17 2016

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)