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A239819 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.

%I A239819 #6 Jun 02 2025 09:32:27
%S A239819 2,4,5,10,23,11,24,132,113,25,56,729,1480,582,57,132,3951,18728,17552,
%T A239819 2981,129,312,21602,232272,510748,204779,15266,293,736,118253,2912793,
%U A239819 14544801,13597573,2405330,78188,665,1736,646306,36627126,418324402
%N A239819 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it, modulo 4.
%C A239819 Table starts
%C A239819 ....2.......4.........10............24................56..................132
%C A239819 ....5......23........132...........729..............3951................21602
%C A239819 ...11.....113.......1480.........18728............232272..............2912793
%C A239819 ...25.....582......17552........510748..........14544801............418324402
%C A239819 ...57....2981.....204779......13597573.........884977259..........58232200212
%C A239819 ..129...15266....2405330.....366379173.......54668820459........8243207656791
%C A239819 ..293...78188...28156167....9807771898.....3347474694032.....1154988223050638
%C A239819 ..665..400542..330152684..263419973152...205970817822022...162794110794893005
%C A239819 .1509.2051667.3868656623.7064275271994.12641836066488239.22871029907841066549
%H A239819 R. H. Hardin, <a href="/A239819/b239819.txt">Table of n, a(n) for n = 1..180</a>
%F A239819 Empirical for column k:
%F A239819 k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
%F A239819 k=2: [order 10]
%F A239819 k=3: [order 35]
%F A239819 Empirical for row n:
%F A239819 n=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A239819 n=2: [order 16]
%F A239819 n=3: [order 64]
%e A239819 Some solutions for n=3 k=4
%e A239819 ..2..0..0..3....3..0..0..0....3..0..2..2....2..3..0..0....3..0..2..2
%e A239819 ..1..0..2..2....1..2..0..0....2..0..1..1....1..3..2..0....1..0..2..0
%e A239819 ..1..2..0..0....2..1..2..3....3..2..3..3....1..0..0..2....3..0..2..0
%Y A239819 Row 1 is A052912
%K A239819 nonn,tabl
%O A239819 1,1
%A A239819 _R. H. Hardin_, Mar 27 2014