A236578 The number of tilings of a 7 X (3n) floor with 1 X 3 trominoes.

1, 9, 155, 2861, 52817, 972557, 17892281, 329097125, 6052932495, 111328274273, 2047599783121, 37660384283749, 692666924307063, 12739845501187821, 234317040993180833, 4309665744385061493, 79265335342431559977

Offset: 0

Author

R. J. Mathar, Jan 29 2014

Keywords

• easy
• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..785
• R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 22.
• R. J. Mathar, Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices, arXiv:1406.7788 [math.CO], 2014, eq. (15).

Crossrefs

Cf. A000930 (3Xn floor), A049086 (4X3n floor), A236576, A236577.

Programs

Maple

p := (x-1)^2*(-x^15 +14*x^14 -104*x^13 +527*x^12 -1971*x^11 +5573*x^10 -11973*x^9 +19465*x^8 -23695*x^7 +21166*x^6 -13512*x^5 +5915*x^4 -1685*x^3 +291*x^2 -27*x+1) ;
q := -17*x^17 +293180*x^8 -236178*x^7 +142400*x^6 -62621*x^5 +19420*x^4 -4062*x^3 +533*x^2 -38*x +x^18 +1 +151*x^16 -946*x^15 +4558*x^14 -17135*x^13 +50164*x^12 -114198*x^11 +202080*x^10 -277277*x^9 ;
taylor(p/q,x=0,30) ;
gfun[seriestolist](%) ;

Formula

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