A240756 Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or zero 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.

5, 6, 12, 16, 16, 35, 35, 36, 65, 83, 102, 172, 191, 230, 381, 458, 576, 905, 1064, 1362, 2090, 2514, 3267, 4869, 5894, 7740, 11297, 13853, 18318, 26249, 32499, 43165, 60950, 76216, 101501, 141589, 178559, 238124, 328924, 418014, 557746, 764306, 977771

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(5 + 6*x + 12*x^2 + x^3 - 2*x^4 - 6*x^5 - 19*x^6 - 24*x^7 - 46*x^8 - 6*x^9 + 7*x^10 + 27*x^11 + 8*x^12 + 5*x^13 - 2*x^14 - x^15 - x^16) / ((1 + x)*(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

Example

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

Crossrefs

Column 2 of A240760.

Sequence in context: A138925 A088767 A032707 * A127306 A319184 A231959

Adjacent sequences: A240753 A240754 A240755 * A240757 A240758 A240759

Keyword

nonn

Author

R. H. Hardin, Apr 12 2014

Status

approved