A240266 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

4, 7, 14, 36, 72, 170, 411, 879, 2106, 4874, 10808, 25648, 58383, 132428, 310199, 704308, 1615735, 3746472, 8529529, 19647966, 45277950, 103456016, 238430432, 547803553, 1255188579, 2890336834, 6633676274, 15225374578, 35023723614

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).

Empirical g.f.: x*(1 + x)*(4 + 3*x + 3*x^2 - 21*x^3 - x^4 - 14*x^5 + 30*x^6 - 4*x^7 + 27*x^8 - x^9 + 2*x^10 - 12*x^11) / (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..0....2..3....3..2....3..0....2..0....2..3....3..2
..3..1....2..1....3..2....3..2....2..1....2..1....2..3....2..0....2..1....3..2
..2..1....3..2....2..3....2..1....3..0....3..1....3..1....3..2....3..2....2..3
..2..0....3..1....3..1....2..1....2..3....2..3....3..2....2..1....3..2....3..2

Crossrefs

Column 2 of A240271.

Sequence in context: A049945 A234576 A076586 * A064961 A137053 A214328

Adjacent sequences: A240263 A240264 A240265 * A240267 A240268 A240269

Keyword

nonn

Author

R. H. Hardin, Apr 03 2014

Status

approved