login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084479 Number of fault-free tilings of a 5 X 3n rectangle with right trominoes. 5
72, 384, 3360, 21504, 163968, 1136640, 8283648, 58791936, 423121920, 3022872576, 21679875072, 155169515520, 1111792499712, 7961492434944, 57028930483200, 408439216748544, 2925470825868288, 20952944438968320, 150073631759459328, 1074876158496638976 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

A tromino is a 3-celled L-shaped piece (a 2 X 2 square with one of the four cells omitted). - N. J. A. Sloane, Mar 28 2017

Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A084478(n).

LINKS

Colin Barker, Table of n, a(n) for n = 2..1000

M. Aanjaneya and S. P. Pal, Faultfree tromino tilings of rectangles, arXiv:math/0610925 [math.CO], 2006.

C. Moore, Some Polyomino Tilings of the Plane, arXiv:math/9905012 [math.CO], 1999.

Index entries for linear recurrences with constant coefficients, signature (2,31,40,20).

FORMULA

G.f.: 24*z^2*(3 + 10*z + 15*z^2) / (1 - 2*z - 31*z^2 - 40*z^3 - 20*z^4).

a(n) = 2*a(n-1) + 31*a(n-2) + 40*a(n-3) + 20*a(n-4) for n > 5. - Colin Barker, Mar 28 2017

MATHEMATICA

LinearRecurrence[{2, 31, 40, 20}, {72, 384, 3360, 21504}, 20] (* Jean-Fran├žois Alcover, Jan 07 2019 *)

PROG

(PARI) Vec(24*x^2*(3 + 10*x + 15*x^2) / (1 - 2*x - 31*x^2 - 40*x^3 - 20*x^4) + O(x^30)) \\ Colin Barker, Mar 28 2017

CROSSREFS

Cf. A084478, A084477, A084480, A084481.

Sequence in context: A090788 A192792 A303621 * A084478 A187158 A164377

Adjacent sequences:  A084476 A084477 A084478 * A084480 A084481 A084482

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, May 27 2003

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 06:19 EDT 2019. Contains 327212 sequences. (Running on oeis4.)