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A239986 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%I A239986 #6 Jun 02 2025 09:36:22
%S A239986 1,1,2,1,3,3,1,4,6,4,1,5,13,16,7,1,6,22,56,40,10,1,7,38,171,261,84,15,
%T A239986 1,8,65,530,1391,935,208,24,1,9,107,1495,7113,9079,4113,474,35,1,10,
%U A239986 169,4059,31226,83658,70107,16724,1047,54,1,11,257,10121,131242,652346
%N A239986 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
%C A239986 Table starts
%C A239986 ..1....1......1........1..........1............1............1............1
%C A239986 ..2....3......4........5..........6............7............8............9
%C A239986 ..3....6.....13.......22.........38...........65..........107..........169
%C A239986 ..4...16.....56......171........530.........1495.........4059........10121
%C A239986 ..7...40....261.....1391.......7113........31226.......131242.......514539
%C A239986 .10...84....935.....9079......83658.......652346......4803152.....33097266
%C A239986 .15..208...4113....70107....1174822.....16721012....226886115...2823199343
%C A239986 .24..474..16724...514297...15307425....381369904...9004871354.198719581101
%C A239986 .35.1047..63746..3533132..192702130...9009351655.404795616742
%C A239986 .54.2530.275188.27478686.2733573580.233083355837
%H A239986 R. H. Hardin, <a href="/A239986/b239986.txt">Table of n, a(n) for n = 1..128</a>
%F A239986 Empirical for column k:
%F A239986 k=1: a(n) = a(n-2) +2*a(n-3)
%F A239986 k=2: a(n) = 2*a(n-2) +10*a(n-3) -a(n-4) -5*a(n-5) -15*a(n-6) +a(n-7) +4*a(n-8) +2*a(n-9) +10*a(n-10) +5*a(n-11) -6*a(n-13)
%F A239986 Empirical for row n:
%F A239986 n=1: a(n) = 1
%F A239986 n=2: a(n) = n + 1
%F A239986 n=3: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3
%F A239986 n=4: [polynomial of degree 10] for n>12
%F A239986 n=5: [polynomial of degree 24] for n>31
%F A239986 n=6: [polynomial of degree 55] for n>73
%e A239986 Some solutions for n=4 k=4
%e A239986 ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0
%e A239986 ..3..1..3..0....2..3..0..3....3..1..3..0....2..1..0..0....2..1..0..0
%e A239986 ..3..1..2..1....2..0..1..2....3..2..0..3....2..0..3..3....2..0..3..0
%e A239986 ..2..1..0..0....3..0..0..1....2..3..0..3....3..2..2..2....2..0..0..3
%Y A239986 Column 1 is A159288
%K A239986 nonn,tabl
%O A239986 1,3
%A A239986 _R. H. Hardin_, Mar 30 2014