login
A184040
1/9 the number of (n+1) X (n+1) 0..2 arrays with all 2 X 2 subblocks having the same four values.
2
9, 21, 41, 81, 153, 297, 569, 1113, 2169, 4281, 8441, 16761, 33273, 66297, 132089, 263673, 526329, 1051641, 2101241, 4200441, 8396793, 16789497, 33570809, 67133433, 134250489, 268484601, 536936441, 1073840121, 2147614713, 4295163897, 8590196729, 17180262393
OFFSET
1,1
FORMULA
From Andrew Howroyd, Mar 09 2024: (Start)
a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
G.f.: x*(9 - 6*x - 22*x^2 + 12*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)). (End)
EXAMPLE
Some solutions for 5X5
..1..0..1..0..1....1..2..1..0..1....1..0..1..0..1....0..1..0..1..0
..1..0..1..0..1....0..0..0..2..0....2..0..2..0..2....1..1..1..1..1
..0..1..0..1..0....1..2..1..0..1....0..1..0..1..0....1..0..1..0..1
..0..1..0..1..0....0..0..0..2..0....0..2..0..2..0....1..1..1..1..1
..0..1..0..1..0....1..2..1..0..1....1..0..1..0..1....0..1..0..1..0
PROG
(PARI) Vec((9 - 6*x - 22*x^2 + 12*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^32)) \\ Andrew Howroyd, Mar 09 2024
CROSSREFS
Diagonal of A184048.
Sequence in context: A338911 A107890 A110209 * A242990 A053476 A110680
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jan 08 2011
EXTENSIONS
a(15) onwards from Andrew Howroyd, Mar 09 2024
STATUS
approved