

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
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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(n1) + 4*a(n2)  a(n4) 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(n1) + 4*a(n2)  a(n4) 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



