A219926 Number of tilings of a 7 X n rectangle using integer-sided square tiles.

1, 1, 21, 129, 1029, 7765, 59257, 450924, 3435392, 26160354, 199243634, 1517411733, 11556549312, 88013947545, 670309228276, 5105035683160, 38879655193542, 296105186372225, 2255119850966932, 17174861374796123, 130802743517191075, 996186073044886758

Offset: 0

Author

Alois P. Heinz, Dec 01 2012

Keywords

• nonn
• easy

Examples

			a(2) = 21, because there are 21 tilings of a 7 X 2 rectangle using integer-sided square tiles:
._._. .___. ._._. ._._. ._._. ._._. ._._. .___. .___. .___. .___.
|_|_| |   | |_|_| |_|_| |_|_| |_|_| |_|_| |   | |   | |   | |   |
|_|_| |___| |   | |_|_| |_|_| |_|_| |_|_| |___| |___| |___| |___|
|_|_| |_|_| |___| |   | |_|_| |_|_| |_|_| |   | |_|_| |_|_| |_|_|
|_|_| |_|_| |_|_| |___| |   | |_|_| |_|_| |___| |   | |_|_| |_|_|
|_|_| |_|_| |_|_| |_|_| |___| |   | |_|_| |_|_| |___| |   | |_|_|
|_|_| |_|_| |_|_| |_|_| |_|_| |___| |   | |_|_| |_|_| |___| |   |
|_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |___| |_|_| |_|_| |_|_| |___|
._._. ._._. ._._. ._._. ._._. ._._. .___. .___. .___. ._._.
|_|_| |_|_| |_|_| |_|_| |_|_| |_|_| |   | |   | |   | |_|_|
|   | |   | |   | |_|_| |_|_| |_|_| |___| |___| |___| |   |
|___| |___| |___| |   | |   | |_|_| |   | |   | |_|_| |___|
|   | |_|_| |_|_| |___| |___| |   | |___| |___| |   | |   |
|___| |   | |_|_| |   | |_|_| |___| |   | |_|_| |___| |___|
|_|_| |___| |   | |___| |   | |   | |___| |   | |   | |   |
|_|_| |_|_| |___| |_|_| |___| |___| |_|_| |___| |___| |___|
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Column k=7 of A219924.

Cf. A226550.

Programs

Maple

gf:= -(6*x^18 -x^17 -9*x^16 +13*x^15 +20*x^14 -35*x^13 -47*x^12 -76*x^11 -145*x^10 -127*x^9 -8*x^8 +64*x^7 +96*x^6 +68*x^5 +7*x^4 -10*x^3 -13*x^2 -2*x +1) / (6*x^25 +11*x^24 -9*x^23 -10*x^22 +39*x^21 +12*x^20 -70*x^19 -281*x^18 -403*x^17 -110*x^16 -118*x^15 -790*x^14 -179*x^13 +466*x^12 +327*x^11 +669*x^10 +1028*x^9 +231*x^8 -45*x^7 -284*x^6 -273*x^5 -61*x^4 +45*x^3 +31*x^2 +3*x -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..30);

Formula

G.f.: see Maple program.