A231242 Number of n X 4 0..3 arrays x(i,j) with each element horizontally, diagonally 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, 44, 464, 5992, 76136, 968824, 12322784, 156753000, 1993963288, 25364073040, 322641895760, 4104143547136, 52206469041840, 664088714466040, 8447493744195456, 107455749517836112, 1366883297468138664

Offset

1,2

Links

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

Formula

Empirical: a(n) = 10*a(n-1) + 30*a(n-2) + 53*a(n-3) + 71*a(n-4) - a(n-5) + 6*a(n-6) - 8*a(n-7).

Empirical g.f.: 4*x^2*(11 + 6*x + 8*x^2 - 9*x^3 - 3*x^4 - 3*x^5) / (1 - 10*x - 30*x^2 - 53*x^3 - 71*x^4 + x^5 - 6*x^6 + 8*x^7). - Colin Barker, Sep 27 2018

Example

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

Crossrefs

Column 4 of A231246.

Sequence in context: A002613 A094201 A210426 * A221730 A306036 A160150

Adjacent sequences: A231239 A231240 A231241 * A231243 A231244 A231245

Keyword

nonn

Author

R. H. Hardin, Nov 06 2013

Status

approved