cp's OEIS Frontend

A281802 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I A281802 #4 Jan 30 2017 10:41:52
%S A281802 0,1,0,0,0,0,3,6,9,0,3,38,75,34,0,9,157,372,324,87,0,15,524,1725,1916,
%T A281802 865,194,0,31,1631,7293,12318,8354,2272,400,0,57,4694,29665,71290,
%U A281802 71445,32524,5191,790,0,108,13006,116539,396185,575062,368408,117401,11141
%N A281802 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C A281802 Table starts
%C A281802 .0....1.....0.......3.........3..........9...........15.............31
%C A281802 .0....0.....6......38.......157........524.........1631...........4694
%C A281802 .0....9....75.....372......1725.......7293........29665.........116539
%C A281802 .0...34...324....1916.....12318......71290.......396185........2143364
%C A281802 .0...87...865....8354.....71445.....575062......4480480.......33526931
%C A281802 .0..194..2272...32524....368408....4173476.....45696162......473403162
%C A281802 .0..400..5191..117401...1770697...28237876....436154254.....6282549989
%C A281802 .0..790.11141..404594...8100180..181908580...3971817891....79584142302
%C A281802 .0.1511.22705.1345667..35778250.1130079060..34908793027...974107985517
%C A281802 .0.2830.44611.4351562.153961577.6826668428.298606378335.11610933931800
%H A281802 R. H. Hardin, <a href="/A281802/b281802.txt">Table of n, a(n) for n = 1..161</a>
%F A281802 Empirical for column k:
%F A281802 k=1: a(n) = a(n-1)
%F A281802 k=2: [order 8] for n>9
%F A281802 k=3: [order 9] for n>16
%F A281802 k=4: [order 44] for n>51
%F A281802 k=5: [order 72] for n>86
%F A281802 Empirical for row n:
%F A281802 n=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
%F A281802 n=2: [order 14]
%F A281802 n=3: [order 60]
%e A281802 Some solutions for n=4 k=4
%e A281802 ..0..1..0..1. .0..0..0..1. .0..1..0..0. .0..0..1..0. .0..1..1..1
%e A281802 ..1..0..1..0. .1..1..1..0. .1..0..1..1. .1..1..0..1. .0..1..1..1
%e A281802 ..0..1..0..0. .1..1..0..0. .0..1..1..0. .1..0..1..0. .0..0..1..1
%e A281802 ..1..1..0..0. .0..0..1..0. .1..1..1..1. .0..0..0..1. .0..0..1..1
%Y A281802 Column 2 is A279128.
%Y A281802 Row 1 is A105423(n-2).
%K A281802 nonn,tabl
%O A281802 1,7
%A A281802 _R. H. Hardin_, Jan 30 2017