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A128102 Number of 2 X 2 tiles in all tilings of a 4 X n rectangle with 1 X 1 and 2 X 2 square tiles. 1
0, 0, 5, 14, 69, 224, 805, 2610, 8545, 27068, 85209, 264406, 814509, 2488536, 7558093, 22827130, 68625657, 205455348, 612884929, 1822355742, 5402974789, 15977195792, 47135117493, 138757706946, 407679684497, 1195641350700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)=Sum(k*A128101(n,k), k=0..2*floor(n/2)).

REFERENCES

S. Heubach, Tiling an m X n area with squares of size up to k X k (m <=5), Congressus Numerantium 140 (1999), pp. 43-64.

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (4,2,-16,-1,12,-4).

FORMULA

G.f.=z^2*(5-6z+3z^2)/(1-2z-3z^2+2z^3)^2.

MAPLE

g:=z^2*(5-6*z+3*z^2)/(1-2*z-3*z^2+2*z^3)^2: gser:=series(g, z=0, 32): seq(coeff(gser, z, n), n=0..29);

CROSSREFS

Cf. A128101.

Sequence in context: A256413 A194994 A166795 * A197901 A202764 A197876

Adjacent sequences:  A128099 A128100 A128101 * A128103 A128104 A128105

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 19 2007

STATUS

approved

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Last modified December 10 20:48 EST 2017. Contains 295856 sequences.