OFFSET
0,3
COMMENTS
As an illustration, here are the figures for n=8 and n=9, respectively.
_ _
_____|_|_____ _______|_|_____
|_|_|_|_|_|_|_|, |_|_|_|_|_|_|_|_|.
LINKS
Index entries for linear recurrences with constant coefficients,signature (1,0,2,0,2,2,0,-1,-1).
FORMULA
a(n) = a(n-1) + 2*a(n-3) + 2*a(n-5) + 2*a(n-6) - a(n-8) - a(n-9).
a(2*n) = a(2*n-1) + a(2*n-3) + a(2*n-4) + 3*a(2*n-5) + 2*a(2*n-6) + a(2*n-7).
a(2*n+1) = a(2*n) + a(2*n-1) + a(2*n-3) + a(2*n-4) + a(2*n-5).
G.f.: x*(1 + x + 2*x^2 + x^3 + x^4 - x^5 - x^6)/(1 - x - 2*x^3 - 2*x^5 -
2*x^6 + x^8 + x^9).
EXAMPLE
For n=8, here is one of a(8)=76 possible tilings with squares, dominos, and flexible trominos.
_
_____| |_____
|___|_|___|___|.
MATHEMATICA
LinearRecurrence[{1, 0, 2, 0, 2, 2, 0, -1, -1}, {0, 1, 2, 4, 7, 12, 21, 40, 76}, 40]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Greg Dresdenand Yinuo Zhu, Jul 17 2024
STATUS
approved