A229750 Number of defective 4-colorings of an n X 3 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order.

1, 60, 598, 2347, 6809, 17404, 41872, 97565, 223075, 503650, 1126490, 2500555, 5515189, 12096536, 26401012, 57368137, 124167191, 267790942, 575680798, 1233926231, 2637709321, 5624580148, 11966370008, 25404922357, 53829723019

Offset

1,2

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 33*a(n-2) + 63*a(n-3) - 66*a(n-4) + 36*a(n-5) - 8*a(n-6) for n>8.

Conjectures from Colin Barker, Sep 21 2018: (Start)

G.f.: x*(1 + 51*x + 91*x^2 - 1118*x^3 + 1706*x^4 - 176*x^5 - 612*x^6 - 64*x^7) / ((1 - x)^3*(1 - 2*x)^3).

a(n) = (2*(1732+117*2^n) + (-4084+279*2^n)*n + (484+9*2^n)*n^2) / 8 for n>2.

(End)

Example

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

Crossrefs

Column 3 of A229755.

Sequence in context: A316458 A184191 A101384 * A223338 A081384 A283786

Adjacent sequences: A229747 A229748 A229749 * A229751 A229752 A229753

Keyword

nonn

Author

R. H. Hardin, Sep 28 2013

Status

approved