A233289 Number of tilings of a 3 X 3 X n box using 3n bricks of shape 3 X 1 X 1.

1, 2, 4, 21, 92, 320, 1213, 4822, 18556, 70929, 273808, 1057020, 4069737, 15676666, 60424640, 232846801, 897164316, 3457096532, 13321674833, 51332757274, 197801848744, 762200458321, 2937024077340, 11317358546188, 43609682555721, 168043191679374

Offset: 0

Author

Alois P. Heinz, Dec 06 2013

Keywords

• nonn
• easy

Comments

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• R. J. Mathar, Tilings of rectangular regions by rectangular tiles: counts derived from transfer matrices, arXiv:1406.7788 [math.CO], 2014; eq. (40).
• Wikipedia, Jenga
• Index entries for linear recurrences with constant coefficients, signature (3,0,13,2,-11,-7,4,-3,1,-1)

Crossrefs

Column k=3 of A233308.

Cf. A006253, A233291, A233294, A273474.

Programs

Maple

gf:= (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):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Formula

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).