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A302150 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A302150 #4 Apr 02 2018 14:28:07
%S A302150 1,1,2,1,1,4,1,2,1,8,1,2,4,1,16,1,3,5,10,1,32,1,6,11,17,28,1,64,1,10,
%T A302150 34,56,65,84,1,128,1,21,88,255,289,257,260,1,256,1,42,271,1038,2005,
%U A302150 1529,1025,816,1,512,1,86,798,4771,12212,15999,8152,4097,2576,1,1024,1,179
%N A302150 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A302150 Table starts
%C A302150 ...1.1....1.....1......1.......1.........1..........1............1
%C A302150 ...2.1....2.....2......3.......6........10.........21...........42
%C A302150 ...4.1....4.....5.....11......34........88........271..........798
%C A302150 ...8.1...10....17.....56.....255......1038.......4771........21866
%C A302150 ..16.1...28....65....289....2005.....12212......83092.......578398
%C A302150 ..32.1...84...257...1529...15999....145150....1482725.....15902462
%C A302150 ..64.1..260..1025...8152..128319...1728734...26544210....439103633
%C A302150 .128.1..816..4097..43676.1030709..20614702..476725579..12181287002
%C A302150 .256.1.2576.16385.234707.8283143.245896061.8575073202.338788296901
%H A302150 R. H. Hardin, <a href="/A302150/b302150.txt">Table of n, a(n) for n = 1..363</a>
%F A302150 Empirical for column k:
%F A302150 k=1: a(n) = 2*a(n-1)
%F A302150 k=2: a(n) = a(n-1)
%F A302150 k=3: a(n) = 4*a(n-1) -2*a(n-2) -2*a(n-3)
%F A302150 k=4: a(n) = 5*a(n-1) -4*a(n-2) for n>3
%F A302150 k=5: [order 12]
%F A302150 k=6: [order 7] for n>9
%F A302150 k=7: [order 51] for n>54
%F A302150 Empirical for row n:
%F A302150 n=1: a(n) = a(n-1)
%F A302150 n=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A302150 n=3: [order 25] for n>27
%F A302150 n=4: [order 85] for n>89
%e A302150 Some solutions for n=5 k=4
%e A302150 ..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..1..1
%e A302150 ..1..1..1..1. .1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..0
%e A302150 ..0..1..1..0. .1..1..1..1. .0..1..1..0. .0..1..1..0. .1..1..1..0
%e A302150 ..0..1..1..1. .0..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e A302150 ..0..1..1..0. .1..1..1..0. .1..1..1..0. .1..1..1..0. .0..1..1..0
%Y A302150 Column 1 is A000079(n-1).
%Y A302150 Column 4 is A052539(n-2).
%Y A302150 Row 2 is A240513(n-3).
%K A302150 nonn,tabl
%O A302150 1,3
%A A302150 _R. H. Hardin_, Apr 02 2018