OFFSET
0,3
COMMENTS
Similar in spirit to A030186, which counts all tilings of a 2 X n board without any restrictions on locations of vertical dominoes.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,9,0,-7,0,1).
FORMULA
a(2*n-1) = Sum_{k=1..2*n-1} k*a(2*n-1-k).
a(2*n-1) = a(2*n-2) + 4*a(2n-3) + a(2*n-4) - a(2*n-5).
a(2*n) = 2*a(2*n-1) + 4*a(2n-2) - a(2*n-4).
G.f.: (1 + 3*x + x^2)*(1 - x)^2/(1 - 9*x^2 + 7*x^4 - x^6).
a(n) = 9*a(n-2) - 7*a(n-4) + a(n-6).
EXAMPLE
This is one of the a(4)=39 possible tilings of a 2 X 4 board. Note that vertical dominoes can only occur in the second or fourth location (we have one vertical domino in the second location in this picture).
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MATHEMATICA
LinearRecurrence[{0, 9, 0, -7, 0, 1}, {1, 1, 5, 10, 39, 83}, 20]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Dresden and Zijie He, Jun 28 2022
STATUS
approved