cp's OEIS Frontend

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

%I A236578 #19 May 01 2017 02:59:45
%S A236578 1,9,155,2861,52817,972557,17892281,329097125,6052932495,111328274273,
%T A236578 2047599783121,37660384283749,692666924307063,12739845501187821,
%U A236578 234317040993180833,4309665744385061493,79265335342431559977
%N A236578 The number of tilings of a 7 X (3n) floor with 1 X 3 trominoes.
%C A236578 Tilings are counted irrespective of internal symmetry: Tilings that match each other after rotations and/or reflections are counted with their multiplicity.
%H A236578 G. C. Greubel, <a href="/A236578/b236578.txt">Table of n, a(n) for n = 0..785</a>
%H A236578 R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings</a>, arXiv:1311.6135 [math.CO], 2013, Table 22.
%H A236578 R. J. Mathar, <a href="http://arxiv.org/abs/1406.7788">Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices</a>, arXiv:1406.7788 [math.CO], 2014, eq. (15).
%F A236578 G.f.: p(x)/q(x) with polynomials p and q defined in the Maple code.
%p A236578 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) ;
%p A236578 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 ;
%p A236578 taylor(p/q,x=0,30) ;
%p A236578 gfun[seriestolist](%) ;
%Y A236578 Cf. A000930 (3Xn floor), A049086 (4X3n floor), A236576, A236577.
%K A236578 easy,nonn
%O A236578 0,2
%A A236578 _R. J. Mathar_, Jan 29 2014