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Search: id:A086347
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| A086347 |
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On a 3 X 3 board, number of n-move routes of chess king ending at a given side cell. |
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+0
8
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| 1, 5, 24, 116, 560, 2704, 13056, 63040, 304384, 1469696, 7096320, 34264064, 165441536, 798822400, 3857055744, 18623512576, 89922273280, 434183143424, 2096421666816, 10122419240960
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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n=1 corresponds to start cell.
Number of aa-avoiding words of length n on alphabet {a,b,c,d,e}. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Joerg Arndt, Fxtbook
Tanya Khovanova, Recursive Sequences
Mike Oakes, KingMovesForPrimes.
Zak Seidov, KingMovesForPrimes.
Sleephound, KingMovesForPrimes.
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FORMULA
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a(n)=(Sqrt[2]/32)((2+Sqrt[8])^(n+1)-(2-Sqrt[8])^(n+1))
G.f.: x(1+x)/(1-4*x-4*x^2). a(n) = A057087(n-1) + A057087(n-2). - R. Stephan, Feb 01 2004
a(n) = 4a(n-1) + 4a(n-2). - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007
a(n)=second binomial transform of 1,3,8,24,64,192 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009]
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EXAMPLE
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a(3)=116 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009]
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MATHEMATICA
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Table[(Sqrt[2]/32)((2+Sqrt[8])^(n+1)-(2-Sqrt[8])^(n+1)), {n, 1, 20}]
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CROSSREFS
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Cf. A086346, A086348.
Cf. A028859: a(n+2) = 2 a(n+1) + 2 a(n).
Sequence in context: A026388 A057969 A004254 this_sequence A026707 A110190 A026784
Adjacent sequences: A086344 A086345 A086346 this_sequence A086348 A086349 A086350
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Jul 17 2003
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EXTENSIONS
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More terms from Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007
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