A239980 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

1, 3, 6, 16, 40, 84, 208, 474, 1047, 2530, 5668, 12907, 30446, 68427, 157875, 366480, 830089, 1920870, 4421253, 10083067, 23303103, 53453752, 122448587, 282350403, 647215090, 1486007814, 3420002865, 7842656682, 18022838258, 41428828907

Offset

1,2

Links

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

Formula

Empirical: 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 g.f.: x*(1 + 3*x + 4*x^2 - x^4 + 4*x^6 - 4*x^7 - 6*x^8 + 6*x^9 + 6*x^10 - 4*x^12) / (1 - 2*x^2 - 10*x^3 + x^4 + 5*x^5 + 15*x^6 - x^7 - 4*x^8 - 2*x^9 - 10*x^10 - 5*x^11 + 6*x^13). - Colin Barker, Oct 26 2018

Example

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

Crossrefs

Column 2 of A239986.

Sequence in context: A168317 A188442 A046211 * A205770 A301959 A018022

Adjacent sequences: A239977 A239978 A239979 * A239981 A239982 A239983

Keyword

nonn

Author

R. H. Hardin, Mar 30 2014

Status

approved