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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

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).

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

EXAMPLE

For n=4, a(4) = 150 = 2*a(3) + 4*a(2) - a(0).

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 *)

PROG

(PARI) Vec((2 - x^2) / ((1 + x)*(1 - 3*x - x^2 + x^3)) + O(x^30)) \\ Colin Barker, Jul 12 2018

CROSSREFS

Cf. A033505.

Sequence in context: A072206 A296255 A277508 * A308345 A280065 A188228

Adjacent sequences:  A316723 A316724 A316725 * A316727 A316728 A316729

KEYWORD

nonn,easy

AUTHOR

Zijing Wu, Jul 11 2018

EXTENSIONS

More terms from Colin Barker, Jul 12 2018

STATUS

approved

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)