A231105 Number of n X 5 0..3 arrays x(i,j) with each element horizontally 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, 20, 286, 4674, 75346, 1217338, 19662930, 317613674, 5130366434, 82870087802, 1338588795186, 21622035453578, 349257679719938, 5641509890213146, 91126511137632082, 1471953642505880106, 23776258946350540066

Offset

1,2

Links

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

Formula

Empirical: a(n) = 14*a(n-1) + 35*a(n-2) - 4*a(n-3) + 4*a(n-4) + 32*a(n-5) - 32*a(n-6).

Empirical g.f.: 2*x^2*(10 + 3*x - 15*x^2 - 10*x^3 - 16*x^4) / ((1 + 2*x)*(1 - 16*x - 3*x^2 + 10*x^3 - 24*x^4 + 16*x^5)). - Colin Barker, Sep 26 2018

Example

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

Crossrefs

Column 5 of A231108.

Sequence in context: A016317 A021404 A046175 * A016314 A021164 A225829

Adjacent sequences: A231102 A231103 A231104 * A231106 A231107 A231108

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved