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Search: id:A054857
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| A054857 |
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Number of ways to tile a 5 X n region with square tiles of size up to 5 X 5. |
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+0
4
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| 1, 1, 8, 28, 117, 472, 1916, 7765, 31497, 127707, 517881, 2100025, 8515772, 34532063, 140030059, 567832091, 2302600696, 9337214060, 37863085664, 153537580071, 622606110920, 2524713292359, 10237896957896, 41515420557135
(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), a(0)=a(1)=1, b(n) as defined in A054858
Cojecture: a(n) = 2*a(n-1) +7*a(n-2) +6*a(n-3) -a(n-4) -5*a(n-5) -2*a(n-6) -3*a(n-7) -a(n-8). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2008]
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EXAMPLE
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a(2)=8 as there is 1 tiling of a 5 X 2 region 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, B[ [ -1 ] ] + B[ [ -2 ] ] + B[ [ -3 ] ] ]} ]; NumOfTilings[ n_ ] := Nest[ f, {{1, 1, 8, 28, 117, 472, 1916, 7765}, {1, 7, 13, 20, 35, 66, 118, 218}}, n - 2 ][ [ 1 ] ] NumOfTilings[ 30 ]
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CROSSREFS
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Cf. A002478, A054856, A054858.
Sequence in context: A095857 A054114 A110687 this_sequence A110046 A027380 A058289
Adjacent sequences: A054854 A054855 A054856 this_sequence A054858 A054859 A054860
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KEYWORD
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nonn,new
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AUTHOR
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Silvia Heubach (silvi(AT)cine.net), Apr 21 2000
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