A229472 Number of defective 4-colorings of an n X 1 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.

0, 1, 2, 6, 20, 70, 246, 854, 2920, 9846, 32810, 108262, 354300, 1151462, 3720094, 11957430, 38263760, 121965718, 387420498, 1226831558, 3874204900, 12203745414, 38354628422, 120294061846, 376572715320, 1176789735350, 3671583974266

Offset

1,3

Comments

Column 1 of A229479.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4) for n>6.

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: x^2*(1 - 6*x + 12*x^2 - 8*x^3 + 3*x^4) / ((1 - x)^2*(1 - 3*x)^2).

a(n) = (27+3^n) * (n-1) / 54 for n>2.

(End)

Example

All solutions for n=4:
  0      0      0      0      0      0
  0      1      1      1      1      0
  1      0      1      2      1      1
  0      0      2      2      0      2

Crossrefs

Cf. A229479.

Sequence in context: A150124 A045631 A275046 * A135413 A193653 A147748

Adjacent sequences: A229469 A229470 A229471 * A229473 A229474 A229475

Keyword

nonn

Author

R. H. Hardin, Sep 24 2013

Status

approved