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

Author

R. H. Hardin, Mar 30 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A159288

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