A233289 - OEIS

%I #29 May 14 2018 11:30:26

%S 1,2,4,21,92,320,1213,4822,18556,70929,273808,1057020,4069737,

%T 15676666,60424640,232846801,897164316,3457096532,13321674833,

%U 51332757274,197801848744,762200458321,2937024077340,11317358546188,43609682555721,168043191679374

%N Number of tilings of a 3 X 3 X n box using 3n bricks of shape 3 X 1 X 1.

%C This is a variant of the Jenga game (see link).

%H Alois P. Heinz, <a href="/A233289/b233289.txt">Table of n, a(n) for n = 0..1000</a>

%H R. J. Mathar, <a href="https://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. (40).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Jenga">Jenga</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,13,2,-11,-7,4,-3,1,-1)

%F G.f.: (x^7 -x^6 +x^5 -x^4 +4*x^3 +2*x^2 +x -1) / (-x^10 +x^9 -3*x^8 +4*x^7 -7*x^6 -11*x^5 +2*x^4 +13*x^3 +3*x -1).

%p gf:= (x^7-x^6+x^5-x^4+4*x^3+2*x^2+x-1)/(-x^10+x^9

%p      -3*x^8+4*x^7-7*x^6-11*x^5+2*x^4+13*x^3+3*x-1):

%p a:= n-> coeff(series(gf, x, n+1), x, n):

%p seq(a(n), n=0..30);

%Y Column k=3 of A233308.

%Y Cf. A006253, A233291, A233294, A273474.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Dec 06 2013