A222139 Number of n X 3 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero.

16, 676, 28564, 1206964, 50999956, 2154990196, 91058563924, 3847656513844, 162581749707796, 6869850581244916, 290283793189916884, 12265868026121849524, 518291141165452870036, 21900260661415244606836

Offset

1,1

Comments

Column 3 of A222144.

Links

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

Formula

Empirical: a(n) = 45*a(n-1) - 116*a(n-2).

Conjectures from Colin Barker, Mar 14 2018: (Start)

G.f.: 4*x*(4 - 11*x) / (1 - 45*x + 116*x^2).

a(n) = (2^(-1-n)*((45-sqrt(1561))^n*(-433+11*sqrt(1561)) + (45+sqrt(1561))^n*(433+11*sqrt(1561)))) / (29*sqrt(1561)).

(End)

Example

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

Crossrefs

Cf. A222144.

Sequence in context: A253126 A014733 A053907 * A036513 A123824 A198283

Adjacent sequences: A222136 A222137 A222138 * A222140 A222141 A222142

Keyword

nonn

Author

R. H. Hardin, Feb 09 2013

Status

approved