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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, 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).
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
Sequence in context: A163419 A375316 A371668 * A236584 A369547 A072743
KEYWORD
nonn,easy
AUTHOR
Sujay Champati and Greg Dresden, Aug 29 2020
STATUS
approved