A233291 Number of tilings of a 4 X 4 X n box using 4n bricks of shape 4 X 1 X 1.
1, 2, 4, 8, 45, 248, 1032, 3524, 13173, 54274, 228712, 917992, 3608665, 14286188, 57438652, 231343468, 926921081, 3700936774, 14793198332, 59241396140, 237333611629, 950127617692, 3801974385964, 15215432779936, 60907523900693, 243826775063490, 976008753961184
Offset: 0
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. (52).
Formula
G.f.: (x^31 -x^30 -x^29 -3*x^28 -5*x^27 +8*x^26 +3*x^25 -39*x^24 +48*x^23 +34*x^22 -11*x^21 +112*x^20 -63*x^19 -34*x^18 +166*x^17 -188*x^16 -174*x^15 +151*x^14 -251*x^13 +57*x^12 +104*x^11 +171*x^10 -69*x^9 -90*x^8 -30*x^7 -61*x^6 +20*x^5 +31*x^4 +4*x^3 +4*x^2 +x -1) / (-x^35 +x^34 +x^33 +5*x^32 +4*x^31 -11*x^30 -10*x^29 +54*x^28 -65*x^27 -48*x^26 -48*x^25 -195*x^24 +231*x^23 -78*x^22 -473*x^21 +794*x^20 +447*x^19 -981*x^18 +1285*x^17 +395*x^16 -720*x^15 -202*x^14 +640*x^13 +567*x^12 -232*x^11 +638*x^10 -169*x^9 -233*x^8 -256*x^7 -97*x^6 +29*x^5 +52*x^4 -4*x^3 +2*x^2 +3*x -1).