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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
- Index entries for linear recurrences with constant coefficients, signature (6,-9).
Programs
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Mathematica
LinearRecurrence[{6,-9},{0,6,28,116},30] (* Harvey P. Dale, Mar 06 2023 *)
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)
Comments