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

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, 1, 8, 65, 530, 1391, 935, 208, 24, 1, 9, 107, 1495, 7113, 9079, 4113, 474, 35, 1, 10, 169, 4059, 31226, 83658, 70107, 16724, 1047, 54, 1, 11, 257, 10121, 131242, 652346

Offset

1,3

Comments

Table starts

..1....1......1........1..........1............1............1............1

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

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

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

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

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

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

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

.35.1047..63746..3533132..192702130...9009351655.404795616742

.54.2530.275188.27478686.2733573580.233083355837

Links

R. H. Hardin, Table of n, a(n) for n = 1..128

Formula

Empirical for column k:

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

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)

Empirical for row n:

n=1: a(n) = 1

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

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

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

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

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

Example

Some solutions for n=4 k=4
..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0
..3..1..3..0....2..3..0..3....3..1..3..0....2..1..0..0....2..1..0..0
..3..1..2..1....2..0..1..2....3..2..0..3....2..0..3..3....2..0..3..0
..2..1..0..0....3..0..0..1....2..3..0..3....3..2..2..2....2..0..0..3

Crossrefs

Column 1 is A159288

Sequence in context: A075195 A293311 A126885 * A285548 A130305 A323346

Adjacent sequences: A239983 A239984 A239985 * A239987 A239988 A239989

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 30 2014

Status

approved