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A318545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A318545 #4 Aug 28 2018 11:07:09
%S A318545 1,2,2,3,1,3,5,3,3,5,8,5,6,5,8,13,8,13,13,8,13,21,15,26,31,26,15,21,
%T A318545 34,26,52,78,78,52,26,34,55,45,107,207,247,207,107,45,55,89,80,218,
%U A318545 516,784,784,516,218,80,89,144,140,442,1288,2349,2905,2349,1288,442,140,144,233
%N A318545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A318545 Table starts
%C A318545 ..1..2...3....5.....8.....13.....21......34.......55........89........144
%C A318545 ..2..1...3....5.....8.....15.....26......45.......80.......140........245
%C A318545 ..3..3...6...13....26.....52....107.....218......442.......899.......1829
%C A318545 ..5..5..13...31....78....207....516....1288.....3270......8271......20866
%C A318545 ..8..8..26...78...247....784...2349....7191....22268.....68384.....210050
%C A318545 .13.15..52..207...784...2905..10496...38721...144148....531780....1960675
%C A318545 .21.26.107..516..2349..10496..46165..208159...942764...4213744...18870716
%C A318545 .34.45.218.1288..7191..38721.208159.1143583..6263377..33963639..184912113
%C A318545 .55.80.442.3270.22268.144148.942764.6263377.41368803.271753441.1792754281
%H A318545 R. H. Hardin, <a href="/A318545/b318545.txt">Table of n, a(n) for n = 1..924</a>
%F A318545 Empirical for column k:
%F A318545 k=1: a(n) = a(n-1) +a(n-2)
%F A318545 k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5) for n>6
%F A318545 k=3: a(n) = a(n-1) +3*a(n-3) +a(n-4) +3*a(n-5) +a(n-7) for n>8
%F A318545 k=4: [order 13] for n>14
%F A318545 k=5: [order 23] for n>24
%F A318545 k=6: [order 37] for n>38
%F A318545 k=7: [order 63] for n>64
%e A318545 Some solutions for n=5 k=4
%e A318545 ..0..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
%e A318545 ..0..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A318545 ..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..0
%e A318545 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1. .1..0..0..1
%e A318545 ..0..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%Y A318545 Column 1 is A000045(n+1).
%Y A318545 Column 2 is A193147.
%K A318545 nonn,tabl
%O A318545 1,2
%A A318545 _R. H. Hardin_, Aug 28 2018