A230905 Number of n X 3 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

0, 8, 38, 152, 634, 2676, 11324, 47954, 203122, 860468, 3645314, 15443536, 65428104, 277194538, 1174373490, 4975404002, 21079033716, 89304460158, 378351663280, 1602943325236, 6791108946594, 28771548268074, 121894966018398

Offset

1,2

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 37*a(n-2) + 65*a(n-3) - 51*a(n-4) + 2*a(n-5) + 20*a(n-6) - 10*a(n-7) + 4*a(n-8) for n>11.

Empirical g.f.: 2*x^2*(4 - 21*x + 34*x^2 - 51*x^4 + 32*x^5 + 16*x^6 - 10*x^7 + x^8 - x^9) / ((1 - 2*x)*(1 - 8*x + 21*x^2 - 23*x^3 + 5*x^4 + 8*x^5 - 4*x^6 + 2*x^7)). - Colin Barker, Sep 22 2018

Example

Some solutions for n=4:
..0..2..1....0..1..0....0..1..0....0..3..2....0..2..1....0..1..3....0..1..3
..1..3..2....2..3..2....3..2..1....1..0..1....1..3..0....3..2..0....3..2..0
..2..0..1....1..0..3....1..0..3....2..3..2....0..1..2....0..1..2....1..3..1
..1..3..2....3..1..2....3..2..1....1..0..1....3..0..3....3..0..3....0..2..0

Crossrefs

Column 3 of A230910.

Sequence in context: A038799 A156934 A036684 * A026640 A122682 A225429

Adjacent sequences: A230902 A230903 A230904 * A230906 A230907 A230908

Keyword

nonn

Author

R. H. Hardin, Nov 01 2013

Status

approved