A316726 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.
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
Offset: 0
Examples
For n=4, a(4) = 150 = 2*a(3) + 4*a(2) - a(0).
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,4,0,-1).
Programs
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Mathematica
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 *) -
PARI
Vec((2 - x^2) / ((1 + x)*(1 - 3*x - x^2 + x^3)) + O(x^30)) \\ Colin Barker, Jul 12 2018
Formula
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
Extensions
More terms from Colin Barker, Jul 12 2018
Comments