A196073 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,2,1,4 for x=0,1,2,3,4.

0, 2, 1, 1, 6, 8, 12, 28, 36, 63, 147, 216, 400, 746, 1204, 2234, 4103, 6927, 12582, 22430, 38914, 70334, 124820, 219139, 392271, 694562, 1227704, 2190008, 3878528, 6871416, 12222729, 21659291, 38421292, 68259422, 121017534, 214735198, 381233984

Offset

1,2

Comments

Every 0 is next to 0 0's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 4's.

Column 3 of A196078.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-2) +2*a(n-3) +a(n-4) +3*a(n-5) +6*a(n-6) -2*a(n-7) -7*a(n-8) -3*a(n-9) -4*a(n-10) -3*a(n-11) +a(n-12) +4*a(n-13) +a(n-14) +a(n-15) -2*a(n-17).

Empirical g.f.: x^2*(2 + x - x^2 + x^3 + 3*x^4 - 3*x^5 - 8*x^6 - 3*x^7 - 5*x^8 - 2*x^9 - x^10 + 6*x^11 + 2*x^13 - 2*x^15) / (1 - x^2 - 2*x^3 - x^4 - 3*x^5 - 6*x^6 + 2*x^7 + 7*x^8 + 3*x^9 + 4*x^10 + 3*x^11 - x^12 - 4*x^13 - x^14 - x^15 + 2*x^17). - Colin Barker, May 08 2018

Example

All solutions for n=4:
..0..1..0
..1..3..1
..1..3..1
..0..1..0

Crossrefs

Cf. A196078.

Sequence in context: A288025 A137376 A039761 * A144089 A172107 A349226

Adjacent sequences: A196070 A196071 A196072 * A196074 A196075 A196076

Keyword

nonn

Author

R. H. Hardin, Sep 27 2011

Status

approved