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A239858 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

%I A239858 #6 Jun 02 2025 09:35:07
%S A239858 2,2,2,4,3,4,6,9,5,6,8,12,44,4,8,14,29,78,84,5,14,20,63,255,203,130,5,
%T A239858 20,30,100,742,1114,484,343,6,30,48,215,1382,3463,4549,1757,685,10,48,
%U A239858 70,468,5647,9963,19065,28184,4979,1704,11,70,108,785,14755,71695,77212
%N A239858 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
%C A239858 Table starts
%C A239858 ..2..2....4......6........8........14.........20..........30.........48
%C A239858 ..2..3....9.....12.......29........63........100.........215........468
%C A239858 ..4..5...44.....78......255.......742.......1382........5647......14755
%C A239858 ..6..4...84....203.....1114......3463.......9963.......71695.....219708
%C A239858 ..8..5..130....484.....4549.....19065......77212......970717....4024283
%C A239858 .14..5..343...1757....28184....176208.....937154....23072270..141040759
%C A239858 .20..6..685...4979...125255...1162638....9885999...421824199.5282952362
%C A239858 .30.10.1704..19850...860559..11924924..147826427.14757679494
%C A239858 .48.11.3977..68830..4802971.111900643.2030390429
%C A239858 .70.15.7958.207822.24477675.995175724
%H A239858 R. H. Hardin, <a href="/A239858/b239858.txt">Table of n, a(n) for n = 1..126</a>
%F A239858 Empirical for column k:
%F A239858 k=1: a(n) = a(n-2) +2*a(n-3)
%F A239858 k=2: a(n) = a(n-2) +a(n-5) for n>9
%F A239858 Empirical for row n:
%F A239858 n=1: a(n) = a(n-2) +2*a(n-3)
%F A239858 n=2: [order 17] for n>21
%e A239858 Some solutions for n=4 k=4
%e A239858 ..3..2..3..3....2..3..3..2....2..3..3..3....3..2..2..2....2..3..2..2
%e A239858 ..2..1..1..2....3..1..1..3....3..1..1..2....2..1..0..0....3..1..1..0
%e A239858 ..3..0..2..2....3..1..1..2....3..2..2..2....3..1..3..0....2..1..2..0
%e A239858 ..3..2..0..0....2..3..0..2....2..3..0..0....2..3..3..3....2..0..0..3
%K A239858 nonn,tabl
%O A239858 1,1
%A A239858 _R. H. Hardin_, Mar 28 2014