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A262274 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.

%I A262274 #4 Sep 17 2015 08:23:06
%S A262274 2,4,4,7,16,7,13,49,49,13,26,169,149,169,26,52,676,585,585,676,52,103,
%T A262274 2704,3639,3253,3639,2704,103,205,10609,23977,37061,37061,23977,10609,
%U A262274 205,410,42025,129481,467065,828152,467065,129481,42025,410,820,168100
%N A262274 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.
%C A262274 Table starts
%C A262274 ...2......4........7.........13............26..............52.............103
%C A262274 ...4.....16.......49........169...........676............2704...........10609
%C A262274 ...7.....49......149........585..........3639...........23977..........129481
%C A262274 ..13....169......585.......3253.........37061..........467065.........4403641
%C A262274 ..26....676.....3639......37061........828152........20331508.......411861253
%C A262274 ..52...2704....23977.....467065......20331508......1002110608.....41261408089
%C A262274 .103..10609...129481....4403641.....411861253.....41261408089...3605017226155
%C A262274 .205..42025...762529...49793329....9709537177...1965295140265.349760937840517
%C A262274 .410.168100..4977703..628659565..246785045498.100013594816980
%C A262274 .820.672400.33121201.8114855785.6349411267540
%H A262274 R. H. Hardin, <a href="/A262274/b262274.txt">Table of n, a(n) for n = 1..112</a>
%F A262274 Empirical for column k:
%F A262274 k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
%F A262274 k=2: [order 8]
%F A262274 k=3: [order 53]
%e A262274 Some solutions for n=4 k=4
%e A262274 ..0..0..1..1..1..1....0..0..0..0..0..0....0..0..1..0..1..0....1..1..0..0..1..0
%e A262274 ..1..0..1..0..0..0....0..0..0..0..0..0....0..0..0..1..0..1....0..1..0..1..0..0
%e A262274 ..0..0..0..1..0..1....0..1..1..0..0..1....0..0..1..0..1..0....1..1..0..0..1..0
%e A262274 ..1..0..1..1..0..1....1..1..0..1..1..1....1..1..0..1..1..1....1..1..1..1..0..0
%e A262274 ..0..0..1..0..1..0....0..1..1..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0
%e A262274 ..0..0..1..1..1..1....1..1..0..1..1..1....1..1..0..0..1..0....1..0..1..0..0..0
%K A262274 nonn,tabl
%O A262274 1,1
%A A262274 _R. H. Hardin_, Sep 17 2015