OFFSET
1,2
COMMENTS
It is assumed that 1 X 1 squares and 1 X 1 strips can be distinguished. - Alois P. Heinz, Feb 23 2022
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
FORMULA
a(n) = 2*3^n + 12*2^n - 19, for n >= 3.
From Colin Barker, Jun 14 2020: (Start)
G.f.: x*(1 + 10*x + 46*x^2 - 281*x^3 + 186*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>5.
(End)
EXAMPLE
Here is one of the 131 ways to tile a 3 X 3 square, in this case using two horizontal and two vertical strips:
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MATHEMATICA
Join[{1, 16}, LinearRecurrence[{6, -11, 6}, {131, 335, 851}, 25]] (* Amiram Eldar, Jun 16 2020 *)
PROG
(PARI) Vec(x*(1 + 10*x + 46*x^2 - 281*x^3 + 186*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Jun 14 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Oluwatobi Jemima Alabi, Jun 14 2020
STATUS
approved