A229587 Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order

0, 6, 28, 116, 444, 1620, 5724, 19764, 67068, 224532, 743580, 2440692, 7951932, 25745364, 82904796, 265720500, 848179836, 2697594516, 8551948572, 27033340788, 85232507580, 268094978388, 841477302108, 2636009007156, 8242758323964

Offset

1,2

Comments

Row 2 of A229586.

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

a(n) = 6*a(n-1) - 9*a(n-2) for n>4.

From Oboifeng Dira, Mar 04 2015: (Start)

a(n) = 4*(3^(n-2) + 4*(2*n-3)*3^(n-4)) for n>2.

G.f.: (x + x^3 + 2*x^4)/(1-3*x)^2 (except for first term).

(End)

Example

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

Mathematica

LinearRecurrence[{6, -9}, {0, 6, 28, 116}, 30] (* Harvey P. Dale, Mar 06 2023 *)

Crossrefs

Sequence in context: A027106 A309717 A089096 * A230492 A026014 A332208

Adjacent sequences: A229584 A229585 A229586 * A229588 A229589 A229590

Keyword

nonn

Author

R. H. Hardin, Sep 26 2013

Status

approved