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.
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
Examples
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
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).
Crossrefs
Diagonal of A184048.
Programs
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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
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)
Extensions
a(15) onwards from Andrew Howroyd, Mar 09 2024