A240322 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

2, 5, 17, 37, 80, 213, 443, 1028, 2511, 5370, 12742, 29737, 65687, 155443, 355668, 803696, 1883007, 4285398, 9805203, 22760901, 51853646, 119272787, 275149593, 628629688, 1447871151, 3328934761, 7625189365, 17555754237, 40308328871

Offset

1,1

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) for n>14.

Empirical g.f.: x*(2 + 5*x + 13*x^2 + 7*x^3 - 2*x^4 - 16*x^5 - 15*x^6 - 3*x^7 + 2*x^8 + 11*x^9 + 13*x^10 + 3*x^11 - 3*x^12 - 4*x^13) / (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 27 2018

Example

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

Crossrefs

Column 2 of A240327.

Sequence in context: A379517 A078523 A078324 * A346809 A276460 A002496

Adjacent sequences: A240319 A240320 A240321 * A240323 A240324 A240325

Keyword

nonn

Author

R. H. Hardin, Apr 03 2014

Status

approved