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 A233036 The maximum number of I-tetrominoes that can be packed into an n X n array of squares when rotation is allowed. 4
 0, 0, 0, 4, 6, 8, 12, 16, 20, 24, 30, 36, 42, 48, 56, 64, 72, 80, 90, 100, 110, 120, 132, 144, 156, 168, 182, 196, 210, 224, 240, 256, 272, 288, 306, 324, 342, 360, 380, 400, 420, 440, 462, 484, 506, 528, 552, 576, 600, 624, 650, 676, 702, 728, 756, 784, 812, 840, 870, 900, 930, 960, 992, 1024, 1056 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A233035. Sequence in context: A076082 A162648 A225512 * A062554 A020225 A310663 Adjacent sequences:  A233033 A233034 A233035 * A233037 A233038 A233039 KEYWORD nonn,easy AUTHOR Kival Ngaokrajang, Dec 03 2013 EXTENSIONS Corrected by Robert Israel, Oct 15 2015 STATUS approved

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Last modified February 24 10:37 EST 2020. Contains 332209 sequences. (Running on oeis4.)