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A316726
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The number of ways to tile (with squares and rectangles) a 2 X (n+2) strip with the upper left and upper right squares removed.
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2
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2, 4, 15, 46, 150, 480, 1545, 4964, 15958, 51292, 164871, 529946, 1703418, 5475328, 17599457, 56570280, 181834970, 584475732, 1878691887, 6038716422, 19410365422, 62391120800, 200545011401, 644615789580, 2072001259342, 6660074556204, 21407609138375
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OFFSET
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0,1
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COMMENTS
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Each number in the sequence is the partial sum of A033505 (n starts at 0, each number add one if n is even). We can also find the recursion relation a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4) for the sequence, which can be proved by induction.
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4) for n>=4.
G.f.: (2 - x^2) / ((1 + x)*(1 - 3*x - x^2 + x^3)). - Colin Barker, Jul 12 2018
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EXAMPLE
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For n=4, a(4) = 150 = 2*a(3) + 4*a(2) - a(0).
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MATHEMATICA
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CoefficientList[ Series[(-x^2 + 1)/(x^4 - 4x^2 - 2x + 1), {x, 0, 27}], x] (* or *) LinearRecurrence[{2, 4, 0, -1}, {2, 4, 15, 46}, 27] (* Robert G. Wilson v, Jul 15 2018 *)
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PROG
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(PARI) Vec((2 - x^2) / ((1 + x)*(1 - 3*x - x^2 + x^3)) + O(x^30)) \\ Colin Barker, Jul 12 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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