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Search: id:A137200
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| A137200 |
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Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type. |
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+0
2
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| 1, 1, 2, 2, 4, 5, 7, 9, 13, 18, 25, 34, 47, 65, 90, 124, 171, 236, 326, 450, 621, 857, 1183, 1633, 2254, 3111, 4294, 5927, 8181, 11292, 15586, 21513, 29694, 40986, 56572, 78085, 107779, 148765, 205337, 283422, 391201, 539966, 745303, 1028725, 1419926, 1959892
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Without the restriction one gets the Fibonacci numbers, A000045.
Might be called the no-tri-bonacci numbers.
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LINKS
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Brian Rice, Proof of the recurrence
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FORMULA
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a(n) = a(n-1) + a(n-4) for n>4; g.f.: (1+x^2+x^4)/(1-x-x^4). Also a(n) = a(n-2) + a(n-4) + a(n-5).
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EXAMPLE
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For example (using 1's to denote squares and 2's to denote dominoes), a(6)=7 because you have the tilings 11211, 1122, 1212, 1221, 2112, 2121, and 2211 and no others.
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CROSSREFS
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Cf. A000045.
Adjacent sequences: A137197 A137198 A137199 this_sequence A137201 A137202 A137203
Sequence in context: A000726 A128663 A135833 this_sequence A026930 A098859 A034398
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KEYWORD
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nonn
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AUTHOR
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Barry Cipra (bcipra(AT)rconnect.com), Mar 03 2008
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