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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 13

%I

%S 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 1,8,65,530,1391,935,208,24,1,9,107,1495,7113,9079,4113,474,35,1,10,

%U 169,4059,31226,83658,70107,16724,1047,54,1,11,257,10121,131242,652346

%N 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 Table starts

%C ..1....1......1........1..........1............1............1............1

%C ..2....3......4........5..........6............7............8............9

%C ..3....6.....13.......22.........38...........65..........107..........169

%C ..4...16.....56......171........530.........1495.........4059........10121

%C ..7...40....261.....1391.......7113........31226.......131242.......514539

%C .10...84....935.....9079......83658.......652346......4803152.....33097266

%C .15..208...4113....70107....1174822.....16721012....226886115...2823199343

%C .24..474..16724...514297...15307425....381369904...9004871354.198719581101

%C .35.1047..63746..3533132..192702130...9009351655.404795616742

%C .54.2530.275188.27478686.2733573580.233083355837

%H R. H. Hardin, <a href="/A239986/b239986.txt">Table of n, a(n) for n = 1..128</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +2*a(n-3)

%F 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 Empirical for row n:

%F n=1: a(n) = 1

%F n=2: a(n) = n + 1

%F n=3: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3

%F n=4: [polynomial of degree 10] for n>12

%F n=5: [polynomial of degree 24] for n>31

%F n=6: [polynomial of degree 55] for n>73

%e Some solutions for n=4 k=4

%e ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0

%e ..3..1..3..0....2..3..0..3....3..1..3..0....2..1..0..0....2..1..0..0

%e ..3..1..2..1....2..0..1..2....3..2..0..3....2..0..3..3....2..0..3..0

%e ..2..1..0..0....3..0..0..1....2..3..0..3....3..2..2..2....2..0..0..3

%Y Column 1 is A159288

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Mar 30 2014

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Last modified September 17 12:40 EDT 2021. Contains 347477 sequences. (Running on oeis4.)