A337492 a(n) = a(n-1) + 4*a(n-3) + 2*a(n-4) + 2*a(n-5); a(0) = a(1) = a(2) = 1, a(3) = 5, a(4) = 11.

1, 1, 1, 5, 11, 19, 43, 99, 207, 439, 959, 2071, 4439, 9567, 20647, 44463, 95751, 206351, 444631, 957855, 2063687, 4446415, 9579799, 20639519, 44468263, 95807663, 206418167, 444729855, 958176071

Offset

0,4

Comments

Number of tilings of a 3 X n rectangle with 1 X 1 squares and L-shaped tiles (where the L-shaped tile covers 5 squares).

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (1,0,4,2,2).

Formula

G.f.: 1/(1-x-4*x^3-2*x^4-2*x^5). - R. J. Mathar, Sep 03 2020

Sum_{k=0..n} a(k) = (a(n+3)+4*a(n)+2*a(n-1)-1)/8. - Sujay Champati, Sep 05 2020

Example

Here is one of the 11 ways to tile a 3 X 4 rectangle:
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Mathematica

LinearRecurrence[{1, 0, 4, 2, 2}, {1, 1, 1, 5, 11}, 50]

Crossrefs

Cf. A127864, A127867.

Sequence in context: A112794 A163419 A371668 * A236584 A369547 A072743

Adjacent sequences: A337489 A337490 A337491 * A337493 A337494 A337495

Keyword

nonn,easy

Author

Sujay Champati and Greg Dresden, Aug 29 2020

Status

approved