

A236582


The number of tilings of an 8 X n floor with 1 X 4 tetrominoes.


5



1, 1, 1, 1, 7, 15, 25, 37, 100, 229, 454, 811, 1732, 3777, 7858, 15339, 31273, 65536, 136600, 276535, 562728, 1159942, 2400783, 4918159, 10052140, 20627526, 42480474, 87254743, 178855138, 366854368
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OFFSET

0,5


COMMENTS

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


LINKS

Table of n, a(n) for n=0..29.
R. J. Mathar, Paving rectangular regions..., arXiv:1311.6135 [math.CO], 2013, Table 37.
R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], 2014, eq. (28).


FORMULA

G.f.: p(x)/q(x) with polynomials p and q defined in the Maple code.


MAPLE

p := (1x)^3*(x+1)^3*(x^2+1)^3*(x^6x^4x^3x^2+1) ;
q := x^2 13*x^10 5*x^18 +8*x^6 x x^20 9*x^4 +16*x^8 13*x^12 2*x^19 +1 +10*x^14 +5*x^7 +6*x^15 6*x^11 +x^22 +6*x^16 +x^17 +2*x^5 2*x^13 ;
taylor(p/q, x=0, 30) ;
gfun[seriestolist](%) ;


CROSSREFS

Cf. A003269 (4 X n floor), A236579  A236581.
Column k=4 of A250662.
Cf. A251074.
Sequence in context: A284758 A211430 A082111 * A268662 A297954 A298577
Adjacent sequences: A236579 A236580 A236581 * A236583 A236584 A236585


KEYWORD

nonn,easy


AUTHOR

R. J. Mathar, Jan 29 2014


STATUS

approved



