A239987 Number of 3 X n 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.

3, 6, 13, 22, 38, 65, 107, 169, 257, 378, 540, 752, 1024, 1367, 1793, 2315, 2947, 3704, 4602, 5658, 6890, 8317, 9959, 11837, 13973, 16390, 19112, 22164, 25572, 29363, 33565, 38207, 43319, 48932, 55078, 61790, 69102, 77049, 85667, 94993, 105065

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Oct 27 2018: (Start)

G.f.: x*(3 - 9*x + 13*x^2 - 13*x^3 + 13*x^4 - 8*x^5 + x^6 + x^7) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.

(End)

Example

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

Crossrefs

Row 3 of A239986.

Sequence in context: A178097 A361276 A211870 * A048134 A058397 A174369

Adjacent sequences: A239984 A239985 A239986 * A239988 A239989 A239990

Keyword

nonn

Author

R. H. Hardin, Mar 30 2014

Status

approved