OFFSET
1,1
LINKS
R. J. Mathar, Tiling n x m rectangles with 1 x 1 and s x s squares, arXiv:1609.03964 [math.CO], 2016, Section 4.1.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*n^2 + 10*n + 3.
From Stefano Spezia, Aug 18 2020: (Start)
O.g.f.: x*(16 - 13*x + 3*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(3 + 13*x + 3*x^2) - 3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
EXAMPLE
For example, here are two of the 35 ways to tile a 4 X 4 square with 1 X 1 and 2 X 2 squares (where we have dropped the colors):
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MATHEMATICA
Table[3 n^2 + 10 n + 3, {n, 50}] (* Wesley Ivan Hurt, Nov 07 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yutong Li, Aug 11 2020
EXTENSIONS
Edited by Greg Dresden, Aug 18 2020
STATUS
approved