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A318075 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A318075 #4 Aug 15 2018 13:21:01
%S A318075 1,2,2,4,6,4,8,10,10,8,16,20,18,20,16,32,42,41,41,42,32,64,89,81,73,
%T A318075 81,89,64,128,190,179,149,149,179,190,128,256,407,404,372,316,372,404,
%U A318075 407,256,512,873,893,861,854,854,861,893,873,512,1024,1874,2000,2016,2195
%N A318075 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A318075 Table starts
%C A318075 ...1...2....4....8....16.....32.....64.....128......256.......512.......1024
%C A318075 ...2...6...10...20....42.....89....190.....407......873......1874.......4024
%C A318075 ...4..10...18...41....81....179....404.....893.....2000......4516......10125
%C A318075 ...8..20...41...73...149....372....861....2016.....4901.....11698......27986
%C A318075 ..16..42...81..149...316....854...2195....5752....15565.....41364.....110930
%C A318075 ..32..89..179..372...854...3029...9966...31057...102906....339938....1115341
%C A318075 ..64.190..404..861..2195...9966..46884..184156...819263...3703730...15865269
%C A318075 .128.407..893.2016..5752..31057.184156..935951..5311510..30435406..167286074
%C A318075 .256.873.2000.4901.15565.102906.819263.5311510.38183961.285095330.2029620744
%H A318075 R. H. Hardin, <a href="/A318075/b318075.txt">Table of n, a(n) for n = 1..420</a>
%F A318075 Empirical for column k:
%F A318075 k=1: a(n) = 2*a(n-1)
%F A318075 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6
%F A318075 k=3: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) +6*a(n-6) for n>10
%F A318075 k=4: [order 18] for n>21
%F A318075 k=5: [order 29] for n>33
%F A318075 k=6: [order 56] for n>61
%e A318075 Some solutions for n=5 k=4
%e A318075 ..0..1..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..1. .0..1..1..0
%e A318075 ..1..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..1..1. .1..1..0..0
%e A318075 ..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..0
%e A318075 ..1..1..1..1. .0..1..0..0. .0..0..0..1. .0..0..1..1. .0..0..0..0
%e A318075 ..1..1..1..0. .1..0..0..1. .0..0..1..1. .0..0..1..1. .1..1..1..1
%Y A318075 Column 1 is A000079(n-1).
%Y A318075 Column 2 is A317759.
%K A318075 nonn,tabl
%O A318075 1,2
%A A318075 _R. H. Hardin_, Aug 15 2018