OFFSET
1,3
COMMENTS
All terms are even, because groups of ways, which are connected by 90 degrees rotation symmetry, are made up from 4 or 2 ways, so the number of ways will be some 4m+2n, and 4m+2n is even.
LINKS
Nicolas Bělohoubek, Visualization of 3rd term
Nicolas Bělohoubek, 90° rotation groups for 3rd term
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 2*(n - 2)*(4*n^3 - 8*n^2 - 19*n + 32) for n > 1.
G.f.: 2*x^3*(11 + 113*x - 19*x^2 - 9*x^3)/(1 - x)^5. - Stefano Spezia, Oct 03 2021
EXAMPLE
For a(1) and a(2) there are fewer squares on the main square then squares of the 2 L-tiles, so a(1) = a(2) = 0.
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 22, 336, 1422, 3952}, 40] (* Harvey P. Dale, Mar 04 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nicolas Bělohoubek, Oct 02 2021
STATUS
approved