login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
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: A296255 A277508 A332234 * A308345 A280065 A188228
KEYWORD
nonn,easy
AUTHOR
Zijing Wu, Jul 11 2018
EXTENSIONS
More terms from Colin Barker, Jul 12 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)