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

0,3

Links

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

Formula

G.f.: see Maple program.

Example

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

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);

Crossrefs

Column k=7 of A219924.

Cf. A226550.

Sequence in context: A220712 A295916 A124117 * A219739 A228283 A157624

Adjacent sequences: A219923 A219924 A219925 * A219927 A219928 A219929

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 01 2012

Status

approved