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.

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

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);

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -4, 12, -1, -16, 2, 4]^n*[0; 0; 5; 14; 69; 224])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A128101.

Sequence in context: A324011 A194994 A166795 * A304060 A197901 A202764

Adjacent sequences: A128099 A128100 A128101 * A128103 A128104 A128105

Keyword

nonn,easy

Author

Emeric Deutsch, Feb 19 2007

Status

approved