A239358 Number of n X 5 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.

6, 16, 32, 60, 106, 156, 218, 299, 399, 524, 680, 874, 1113, 1404, 1754, 2170, 2659, 3228, 3884, 4634, 5485, 6444, 7518, 8714, 10039, 11500, 13104, 14858, 16769, 18844, 21090, 23514, 26123, 28924, 31924, 35130, 38549, 42188, 46054, 50154, 54495, 59084

Offset

1,1

Links

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

Formula

Empirical: a(n) = (7/6)*n^3 - (39/2)*n^2 + (538/3)*n - 486 for n>8.

Conjectures from Colin Barker, Oct 25 2018: (Start)

G.f.: x*(6 - 8*x + 4*x^2 + 4*x^3 - 20*x^5 + 22*x^6 - x^7 - 7*x^8 + 6*x^9 + x^11) / (1 - x)^4.

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

(End)

Example

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

Crossrefs

Column 5 of A239361.

Sequence in context: A345023 A243763 A061235 * A171494 A201055 A071857

Adjacent sequences: A239355 A239356 A239357 * A239359 A239360 A239361

Keyword

nonn

Author

R. H. Hardin, Mar 17 2014

Status

approved