A226372 Number of tilings of an 8 X n rectangle using integer-sided square tiles of area > 1.

1, 0, 1, 0, 5, 0, 16, 0, 48, 0, 160, 0, 511, 0, 1651, 2, 5341, 4, 17260, 22, 55846, 92, 180658, 322, 584545, 1240, 1891519, 4520, 6120813, 16202, 19807322, 57956, 64098350, 204762, 207430088, 718472, 671273411, 2506702, 2172343071, 8697828, 7030048159

Offset: 0

Author

Alois P. Heinz, Jun 05 2013

Keywords

• nonn
• easy

Examples

			a(4) = 5:
._._._._.  ._._._._.  ._._._._.  ._._._._.  ._._._._.
|       |  |   |   |  |   |   |  |       |  |   |   |
|       |  |___|___|  |___|___|  |       |  |___|___|
|       |  |   |   |  |       |  |       |  |   |   |
|_______|  |___|___|  |       |  |_______|  |___|___|
|       |  |       |  |       |  |   |   |  |   |   |
|       |  |       |  |_______|  |___|___|  |___|___|
|       |  |       |  |   |   |  |   |   |  |   |   |
|_______|  |_______|  |___|___|  |___|___|  |___|___|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=8 of A226206.

Programs

Maple

a:= n-> coeff(series(-(x-1) *(x+1) *(x^3+x-1) *(x^3+x+1) *(x^11 -x^10 +x^9 -x^8 +x^7 -2*x^6 -x^5 +x^4 -x^3 +x^2 -x+1) / (x^27 -x^26 +5*x^25 -5*x^24 +9*x^23 -8*x^22 +3*x^21 -5*x^20 -18*x^19 +12*x^18 -29*x^17 +29*x^16 -17*x^15 +32*x^14 +16*x^13 -13*x^12 +25*x^11 -28*x^10 +15*x^9 -18*x^8 -4*x^7 +5*x^6 -5*x^5 +5*x^4 -2*x^3 +2*x^2 +x-1), x, n+1), x, n):
seq(a(n), n=0..60);

Formula

G.f.: -(x-1) *(x+1) *(x^3+x-1) *(x^3+x+1) *(x^11 -x^10 +x^9 -x^8 +x^7 -2*x^6 -x^5 +x^4 -x^3 +x^2 -x+1) / (x^27 -x^26 +5*x^25 -5*x^24 +9*x^23 -8*x^22 +3*x^21 -5*x^20 -18*x^19 +12*x^18 -29*x^17 +29*x^16 -17*x^15 +32*x^14 +16*x^13 -13*x^12 +25*x^11 -28*x^10 +15*x^9 -18*x^8 -4*x^7 +5*x^6 -5*x^5 +5*x^4 -2*x^3 +2*x^2 +x-1).