A240187 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 three plus the sum of the elements diagonally to its northwest, modulo 4.

1, 5, 12, 27, 73, 154, 358, 872, 1871, 4438, 10338, 22880, 54100, 123711, 279854, 655190, 1491102, 3413413, 7919449, 18045604, 41514375, 95741087, 218782546, 503899032, 1158409848, 2653808377, 6109601340, 14027233372, 32187863462

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 + 5*x + 10*x^2 + 7*x^3 - 10*x^5 - 6*x^6 - 5*x^7 - 6*x^8 + 4*x^9 + 4*x^10 + 6*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:
..2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0....2..0
..1..0....1..0....1..3....2..0....2..0....1..3....1..3....2..0....2..3....1..3
..2..3....2..3....1..2....2..0....2..3....2..1....2..3....2..0....2..3....2..3
..1..2....1..3....2..3....1..0....2..3....1..2....1..0....2..0....1..0....1..2

Crossrefs

Column 2 of A240192.

Sequence in context: A357417 A229422 A128439 * A172426 A145768 A162778

Adjacent sequences: A240184 A240185 A240186 * A240188 A240189 A240190

Keyword

nonn

Author

R. H. Hardin, Apr 02 2014

Status

approved