|
%I #4 Dec 01 2014 07:36:29
%S 8,18,18,38,56,38,84,150,150,84,180,446,464,446,180,394,1232,1770,
%T 1770,1232,394,850,3602,5680,9130,5680,3602,850,1852,10108,21088,
%U 38332,38332,21088,10108,1852,4008,29272,69270,192442,185620,192442,69270,29272,4008
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having a single 1 or two 1s on the same edge
%C Table starts
%C ....8.....18......38.......84........180.........394..........850
%C ...18.....56.....150......446.......1232........3602........10108
%C ...38....150.....464.....1770.......5680.......21088........69270
%C ...84....446....1770.....9130......38332......192442.......836546
%C ..180...1232....5680....38332.....185620.....1215600......6080510
%C ..394...3602...21088...192442....1215600....10753448.....71459218
%C ..850..10108...69270...836546....6080510....71459218....539961360
%C .1852..29272..252226..4112126...38748690...612889014...6151714502
%C .4008..82854..842160.18298862..198765264..4229034766..47962536500
%C .8714.238640.3024532.88585834.1238605998.35355603854.531311887046
%H R. H. Hardin, <a href="/A251258/b251258.txt">Table of n, a(n) for n = 1..611</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +3*a(n-2) -a(n-3)
%F k=2: a(n) = 3*a(n-1) +4*a(n-2) -14*a(n-3) +3*a(n-4) +3*a(n-5)
%F k=3: a(n) = a(n-1) +13*a(n-2) -7*a(n-3) -32*a(n-4) +8*a(n-5) +10*a(n-6)
%F k=4: [order 12]
%F k=5: [order 17]
%F k=6: [order 31]
%F k=7: [order 49]
%e Some solutions for n=4 k=4
%e ..0..1..0..0..0....0..0..1..0..0....0..0..1..0..1....1..0..1..1..0
%e ..0..1..0..1..1....1..0..1..0..1....1..0..0..0..0....1..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....0..0..1..0..1....1..0..1..1..0
%e ..1..1..1..0..1....0..1..0..1..0....1..0..1..0..0....1..0..0..0..0
%e ..0..0..0..0..1....0..1..0..1..0....0..0..1..0..1....1..0..1..1..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
| 