OFFSET
1,4
COMMENTS
By de Bruijn's theorem (see the de Bruijn link), an m X n rectangle can't be tiled with I tetrominoes unless m or n is divisible by 4. - Robert Israel, Oct 15 2015
LINKS
N. G. de Bruijn, "Filling boxes with bricks", The American Mathematical Monthly 76 (1969), 37-40.
Robert Israel, Illustration of initial terms
Wikipedia, Tetromino
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
FORMULA
From Robert Israel, Oct 15 2015: (Start)
a(4*k) = 4*k^2.
a(2*k+1) = k*(k+1) for k >= 2.
a(4*k+2) = 4*k*(k+1).
G.f.: 2*x^3/((1 + x)*(1 + x^2)*(1 - x)^3) - 2*x^3. (End)
Apparently a(n) = A182568(n+2) for n > 3. - Georg Fischer, Oct 14 2018
MAPLE
0$3, seq(op([4*k^2, 2*k*(2*k+1), 4*k*(k+1), (2*k+1)*(2*k+2)]), k=1..20); # Robert Israel, Oct 15 2015
MATHEMATICA
CoefficientList[Series[2 x^3/((1 + x) (1 + x^2) (1 - x)^3) - 2 x^3, {x, 0, 100}], x] (* Vincenzo Librandi, Oct 15 2015 *)
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 0, 0, 4, 6, 8, 12, 16, 20}, 70] (* Harvey P. Dale, Dec 16 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, Dec 03 2013
EXTENSIONS
Corrected by Robert Israel, Oct 15 2015
STATUS
approved