OFFSET
1,3
COMMENTS
Number of ways two dominoes can be placed on an "other" Aztec Diamonds chessboard.
LINKS
Nicolas Bělohoubek, Visualization of 3rd term.
Ron Knott, 1.2.5 The "other" Aztec Diamonds
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 2*(n-2)*(4n^3-8n^2+n+4) for n > 1.
From Stefano Spezia, Aug 17 2021: (Start)
G.f.: 2*x^3*(43 + 57*x - 3*x^2 - x^3)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 6. (End)
EXAMPLE
For n=1 there is no way to place 2 dominoes in the centered square grid graphs, because they don't have enough space to be placed, so a(1)=0.
For n=2 there is no way to place 2 dominoes in the centered square grid graphs, because the first domino will cover the center square every time, so a(2)=0.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nicolas Bělohoubek, Aug 17 2021
STATUS
approved