A265988 Number of n X 4 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

1, 2, 2, 2, 7, 7, 21, 35, 78, 158, 323, 682, 1395, 2920, 6035, 12551, 26048, 54067, 112291, 233073, 483986, 1004757, 2086142, 4331198, 8992360, 18669984, 38762260, 80478161, 167087798, 346906568, 720244459, 1495365541, 3104666070, 6445881590

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + a(n-3) - a(n-5) - 3*a(n-6) + a(n-7).

Empirical g.f.: x*(1 + x - 2*x^2 - 5*x^3 - x^4 - 5*x^5 + 3*x^6) / ((1 - x)*(1 - 2*x^2 - 3*x^3 - 3*x^4 - 2*x^5 + x^6)). - Colin Barker, Jan 09 2019

Example

Some solutions for n=7:
..1..3..1..1....1..3..1..1....1..3..1..1....1..2..2..1....1..3..1..1
..1..1..3..1....1..1..3..1....1..1..4..2....1..1..1..1....1..1..3..1
..1..3..1..1....1..3..1..1....1..3..3..1....1..3..3..1....1..3..1..1
..1..1..4..2....1..1..3..2....1..1..1..1....1..1..1..1....1..1..4..2
..1..3..3..1....1..3..4..1....1..3..3..1....1..3..3..1....1..3..3..1
..1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1....2..4..1..1
..1..2..2..1....1..2..2..1....1..2..2..1....1..2..2..1....1..1..3..1

Crossrefs

Column 4 of A265991.

Sequence in context: A169592 A245600 A266689 * A340976 A023573 A138757

Adjacent sequences: A265985 A265986 A265987 * A265989 A265990 A265991

Keyword

nonn

Author

R. H. Hardin, Dec 19 2015

Status

approved