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A283572 T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

%I A283572 #6 Jul 28 2022 03:27:52
%S A283572 0,0,0,1,4,0,2,26,16,0,5,72,169,68,0,12,282,674,1108,256,0,26,908,
%T A283572 4313,6812,6453,924,0,56,2832,21186,67892,60802,36038,3232,0,118,8856,
%U A283572 104464,509952,945100,528436,194173,11044,0,244,26750,513458,3890056,10919674
%N A283572 T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
%C A283572 Table starts
%C A283572 .0......0........1..........2............5.............12...............26
%C A283572 .0......4.......26.........72..........282............908.............2832
%C A283572 .0.....16......169........674.........4313..........21186...........104464
%C A283572 .0.....68.....1108.......6812........67892.........509952..........3890056
%C A283572 .0....256.....6453......60802.......945100.......10919674........129527524
%C A283572 .0....924....36038.....528436.....12699250......226897932.......4173039716
%C A283572 .0...3232...194173....4441052....164714523.....4558585174.....129997769458
%C A283572 .0..11044..1021432...36589848...2089140956....89724600000....3965206666608
%C A283572 .0..37104..5275885..296555892..26034179747..1736716820366..118919078661476
%C A283572 .0.122984.26869458.2373574616.320066184088.33188681249924.3520469545329364
%H A283572 R. H. Hardin, <a href="/A283572/b283572.txt">Table of n, a(n) for n = 1..241</a>
%F A283572 Empirical for column k:
%F A283572 k=1: a(n) = a(n-1)
%F A283572 k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)
%F A283572 k=3: [order 12]
%F A283572 k=4: [order 16]
%F A283572 k=5: [order 42]
%F A283572 k=6: [order 54]
%F A283572 Empirical for row n:
%F A283572 n=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
%F A283572 n=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)
%F A283572 n=3: [order 12]
%F A283572 n=4: [order 16]
%F A283572 n=5: [order 42]
%F A283572 n=6: [order 64]
%e A283572 Some solutions for n=4, k=4
%e A283572 ..1..1..0..0. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..1..0
%e A283572 ..1..0..0..1. .0..0..0..1. .1..1..0..0. .1..0..0..0. .0..1..1..0
%e A283572 ..0..0..1..0. .0..1..0..1. .1..0..1..0. .0..0..1..1. .1..0..0..0
%e A283572 ..0..0..0..0. .0..1..1..0. .0..0..1..0. .1..0..0..1. .0..0..1..1
%Y A283572 Column 2 is A283036.
%Y A283572 Row 1 is A073778(n-1).
%K A283572 nonn,tabl
%O A283572 1,5
%A A283572 _R. H. Hardin_, Mar 11 2017