A206377 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..3 introduced in row major order.

85, 1369, 25945, 520097, 10690969, 222329489, 4648291369, 97418918945, 2043949959289, 42905465857457, 900849319640905, 18916269750894785, 397226844350640025, 8341623469422864209, 175172765404628220265

Offset

1,1

Comments

Column 2 of A206383.

Links

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

Formula

Empirical: a(n) = 36*a(n-1) - 377*a(n-2) + 1398*a(n-3) - 2064*a(n-4) + 1008*a(n-5).

Empirical g.f.: x*(85 - 1691*x + 8706*x^2 - 16640*x^3 + 10320*x^4) / ((1 - x)*(1 - 2*x)*(1 - 21*x)*(1 - 12*x + 24*x^2)). - Colin Barker, Jun 15 2018

Example

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

Crossrefs

Cf. A206383.

Sequence in context: A297587 A189439 A166917 * A351105 A008360 A212474

Adjacent sequences: A206374 A206375 A206376 * A206378 A206379 A206380

Keyword

nonn

Author

R. H. Hardin, Feb 07 2012

Status

approved