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A302278 T(n,k) = number of n X k 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302278 #7 Apr 05 2018 04:09:22
%S A302278 0,1,0,1,3,0,2,7,10,0,3,10,22,23,0,5,27,29,79,61,0,8,45,74,89,269,162,
%T A302278 0,13,98,162,283,353,942,421,0,21,193,363,649,1219,941,3401,1103,0,34,
%U A302278 379,782,1621,3621,3854,3316,12283,2890,0,55,778,1766,4209,14125,15862,14639
%N A302278 T(n,k) = number of n X k 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302278 Table starts
%C A302278   0    1     1     2      3       5        8       13        21         34
%C A302278   0    3     7    10     27      45       98      193       379        778
%C A302278   0   10    22    29     74     162      363      782      1766       3953
%C A302278   0   23    79    89    283     649     1621     4209      9563      25179
%C A302278   0   61   269   353   1219    3621    14125    38410    108141     360173
%C A302278   0  162   942   941   3854   15862    72083   229708    713848    2948380
%C A302278   0  421  3401  3316  14639   69601   384916  1354563   4386347   20677591
%C A302278   0 1103 12283 12016  63093  385242  3027442 11370253  43394297  258471515
%C A302278   0 2890 43006 34060 222254 1809350 17837758 75667277 325745362 2460590443
%H A302278 R. H. Hardin, <a href="/A302278/b302278.txt">Table of n, a(n) for n = 1..220</a>
%F A302278 Empirical for column k:
%F A302278 k=1: a(n) = a(n-1)
%F A302278 k=2: a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4)
%F A302278 k=3: [order 18]
%F A302278 k=4: [order 72] for n > 73
%F A302278 Empirical for row n:
%F A302278 n=1: a(n) = a(n-1) + a(n-2)
%F A302278 n=2: a(n) = a(n-1) + 3*a(n-2) - 4*a(n-4) for n > 5
%F A302278 n=3: [order 16] for n > 18
%F A302278 n=4: [order 64] for n > 66
%e A302278 Some solutions for n=5, k=4:
%e A302278   0 0 1 1     0 1 1 1     0 0 0 0     0 0 0 0     0 0 1 0
%e A302278   1 1 0 0     0 0 1 0     1 1 1 1     0 1 0 1     1 1 0 0
%e A302278   1 0 1 0     0 0 0 0     0 1 0 1     1 0 1 0     0 0 0 1
%e A302278   1 0 1 0     0 1 1 1     1 0 1 0     1 1 1 1     0 1 1 1
%e A302278   0 1 0 1     1 0 0 0     0 1 0 1     0 0 0 0     1 1 0 0
%Y A302278 Column 2 is A185828.
%Y A302278 Row 1 is A000045(n-1).
%K A302278 nonn,tabl
%O A302278 1,5
%A A302278 _R. H. Hardin_, Apr 04 2018