A239359 Number of n X 6 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 3.

7, 19, 39, 77, 156, 266, 409, 599, 852, 1191, 1635, 2213, 2944, 3837, 4910, 6178, 7657, 9363, 11312, 13520, 16003, 18777, 21858, 25262, 29005, 33103, 37572, 42428, 47687, 53365, 59478, 66042, 73073, 80587, 88600, 97128, 106187, 115793, 125962, 136710

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (8/3)*n^3 - (45/2)*n^2 + (257/6)*n + 330 for n>13.

Conjectures from Colin Barker, Oct 26 2018: (Start)

G.f.: x*(7 - 9*x + 5*x^2 + 7*x^3 + 13*x^4 - 33*x^5 + 12*x^6 + 12*x^7 + 2*x^8 + 7*x^9 - 4*x^10 + 10*x^11 - 10*x^12 - 10*x^13 + 9*x^14 - 3*x^15 + x^16) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>17.

(End)

Example

Some solutions for n=5:
..0..0..0..0..2..2....0..0..0..0..0..0....0..0..0..0..0..0....0..0..2..2..0..0
..0..0..0..2..2..1....0..0..0..0..0..0....0..0..0..0..0..2....0..0..2..1..2..2
..0..0..0..2..1..2....2..2..0..0..0..0....0..0..0..0..0..2....0..0..0..2..2..1
..0..0..0..0..2..2....2..1..2..2..0..0....2..2..0..0..0..0....0..0..0..2..1..2
..2..2..0..0..0..0....0..2..2..1..2..0....2..1..2..2..0..0....2..2..0..0..1..2

Crossrefs

Column 6 of A239361.

Sequence in context: A108766 A303855 A295077 * A120720 A098422 A191066

Adjacent sequences: A239356 A239357 A239358 * A239360 A239361 A239362

Keyword

nonn

Author

R. H. Hardin, Mar 17 2014

Status

approved