A240789 Number of n X 2 0..3 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 zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

3, 4, 5, 10, 13, 14, 30, 32, 36, 67, 79, 97, 173, 191, 232, 402, 464, 580, 960, 1104, 1400, 2250, 2637, 3388, 5280, 6255, 8117, 12342, 14819, 19374, 28826, 35008, 46021, 67233, 82554, 108956, 156715, 194316, 257170, 365065, 456688, 605532, 850096, 1071831

Offset: 1

Author

R. H. Hardin, Apr 12 2014

Keywords

• nonn

Examples

			All solutions for n=4:
..3..3....3..3....3..3....3..3....3..2....3..2....3..3....3..2....3..3....3..3
..2..1....2..2....2..1....2..2....3..1....3..1....2..2....3..1....2..2....2..2
..3..3....3..1....3..3....3..1....2..2....2..1....3..3....2..2....3..1....3..1
..2..2....2..2....2..1....3..2....3..1....3..3....2..2....3..3....3..1....2..1
		

Links

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

Crossrefs

Column 2 of A240792.

Formula

Empirical: a(n) = 4*a(n-3) + a(n-5) - 3*a(n-6) - 3*a(n-8) - 4*a(n-9) + a(n-11) + 4*a(n-12) + 3*a(n-14) - 2*a(n-17) for n>19.

Empirical g.f.: x*(3 + 4*x + 5*x^2 - 2*x^3 - 3*x^4 - 9*x^5 - 5*x^6 - 13*x^7 - 6*x^8 - 12*x^9 + 7*x^10 + 12*x^11 + 26*x^12 + 8*x^13 - 8*x^14 - 17*x^15 - 5*x^16 + 5*x^17 + 2*x^18) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x^2 - x^3)*(1 - 2*x^3)*(1 + x^2 - x^3 + x^4 - x^5)). - Colin Barker, Oct 29 2018