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Search: id:A105262
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| A105262 |
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a(n)=number of tilings of a 4 X n rectangle using tiles that are either 1 X 1 squares or trominoes (here by a tromino we mean a 2 X 2 square with the upper right 1 X 1 square removed; no rotations allowed). |
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+0
1
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| 1, 1, 5, 13, 42, 126, 387, 1180, 3606, 11012, 33636, 102733, 313781, 958384, 2927209, 8940617, 27307465, 83405605, 254747014, 778077690, 2376494563, 7258563604, 22169941574, 67713990832, 206819875428, 631693101321, 1929389878185
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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E. Deutsch, Counting tilings with L-tiles and squares, Problem 10877, Amer. Math. Monthly, 110 (March 2003), 245-246.
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FORMULA
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G.f.=(1-z^2-z^3)/(1-z-5z^2-4z^3+z^5). Rec. eq.: a(n)=a(n-1)+5a(n-2)+4a(n-3)-a(n-5) for n>=5; a(0)=1, a(1)=1, a(2)=5, a(3)=13, a(4)=42.
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MAPLE
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a[0]:=1:a[1]:=1:a[2]:=5:a[3]:=13:a[4]:=42: for n from 5 to 30 do a[n]:=a[n-1]+5*a[n-2]+4*a[n-3]-a[n-5] od: seq(a[n], n=0..30);
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CROSSREFS
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Sequence in context: A111009 A012172 A066873 this_sequence A129789 A093576 A115785
Adjacent sequences: A105259 A105260 A105261 this_sequence A105263 A105264 A105265
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 15 2005
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