login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236579 The number of tilings of a 5 X (4n) floor with 1 X 4 tetrominoes. 3
1, 3, 15, 75, 371, 1833, 9057, 44753, 221137, 1092699, 5399327, 26679563, 131831075, 651413681, 3218814561, 15905050017, 78591236385, 388340962771, 1918899743823, 9481812581835, 46852249642771 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.

Related to A002378 by an Invert Transform.

LINKS

Table of n, a(n) for n=0..20.

R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 34.

R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], eq. (24).

Index entries for linear recurrences with constant coefficients, signature (6,-6,4,-1).

FORMULA

G.f.: (1-x)^3/(-6*x+1+6*x^2-4*x^3+x^4).

a(n) = Sum_{k = 0..n} binomial(n + 3*k, 4*k)*2^k = Sum_{k = 0..n} A109960(n,k)*2^k. - Peter Bala, Nov 02 2017

a(n) = hypergeom([(n+1)/3, (n+2)/3, n/3 + 1, -n], [1/4, 1/2, 3/4], -27/128). - Peter Luschny, Nov 02 2017

MAPLE

g := (1-x)^3/(-6*x+1+6*x^2-4*x^3+x^4) ;

taylor(%, x=0, 30) ; gfun[seriestolist](%) ;

# Alternatively:

a := n -> hypergeom([(n+1)/3, (n+2)/3, n/3 + 1, -n], [1/4, 1/2, 3/4], -27/128):

seq(simplify(a(n)), n=0..20); # Peter Luschny, Nov 02 2017

MATHEMATICA

LinearRecurrence[{6, -6, 4, -1}, {1, 3, 15, 75}, 21] (* Jean-Fran├žois Alcover, Jul 14 2018 *)

CROSSREFS

Cf. A003269 (4Xn floor), A236580 - A236582, A109960.

Sequence in context: A151326 A063000 A002902 * A005053 A329764 A183411

Adjacent sequences:  A236576 A236577 A236578 * A236580 A236581 A236582

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jan 29 2014

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 April 20 09:21 EDT 2021. Contains 343125 sequences. (Running on oeis4.)