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Search: id:A054855
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| A054855 |
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Number of ways to tile a 5 X n area with 1 X 1 and 2 X 2 tiles. |
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8
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| 1, 1, 8, 21, 93, 314, 1213, 4375, 16334, 59925, 221799, 817280, 3018301, 11134189, 41096528, 151643937, 559640289, 2065192514, 7621289593, 28124714395, 103789150046, 383013144129, 1413437041011, 5216013647648, 19248692843977
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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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.
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FORMULA
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a(n)=b(1)a(n-1)+b(2)a(n-2)+...+b(n)a(0), where a(0)=a(1)=1, and b(1)=1, b(2)=7, b(n)=F(n+1)of A000045 (Fibonacci numbers) for n>2
a(n) = 2a(n-1) + 7a(n-2) - 2a(n-3) - 3a(n-4) - Keith Schneider (kschneid(AT)bulldog.unca.edu), Apr 02 2006
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EXAMPLE
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a(2)=8 as there is one tiling of a 5 X 2 area with only 1 X 1 tiles, 4 tilings with exactly one 2 X 2 tile and 3 tilings with exactly two 2 X 2 tiles.
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MATHEMATICA
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f[{A_, B_}] := Module[{til = A, basic = B}, {Flatten[Append[til, ListConvolve[A, B]]], AppendTo[basic, 2 Fibonacci[Length[B] + 2]]}]; NumOfTilings[n_] := Nest[f, {{1, 1}, {1, 7}}, n - 2][[1]] NumOfTilings[30]
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CROSSREFS
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Cf. A054854, A000045.
Sequence in context: A066859 A080144 A096018 this_sequence A100903 A141369 A060390
Adjacent sequences: A054852 A054853 A054854 this_sequence A054856 A054857 A054858
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KEYWORD
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easy,nonn
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AUTHOR
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Silvia Heubach (silvi(AT)cine.net), Apr 21 2000
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