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Search: id:A022026
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| A022026 |
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Define the sequence T(a_0,a_1) by a_{n+2} is the greatest integer such that a_{n+2}/a_{n+1}<a_{n+1}/a_n for n >= 0 . This is T(2,15). |
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1
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| 2, 15, 112, 836, 6240, 46576, 347648, 2594880, 19368448, 144568064, 1079070720, 8054293504, 60118065152, 448727347200, 3349346516992, 24999862747136, 186601515909120, 1392812676284416, 10396095346638848
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OFFSET
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0,1
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COMMENT
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Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 18 2009: (Start)
a(n) is also the number of forests in the 2x(n+1) grid.
a(0)=2, because there are 2 forests in the 2x1 grid: 1.2 and 1-2.
a(1)=15, because there are 15 forests in the 2x2 grid:
1.2 1-2 1.2 1.2 1.2 1-2 1-2 1-2 1.2 1.2 1.2 1.2 1-2 1-2 1-2
. . . . . | . . | . . | . . | . . | | | | . | | | . | | . |
4.3 4.3 4.3 4-3 4.3 4.3 4-3 4.3 4-3 4.3 4-3 4-3 4-3 4.3 4-3
a(n) = 8a(n-1) - 4a(n-2) for n>=2, because each of the a(n-1) forests can be extended by 8 patterns:
.o -o .o -o .o -o .o -o
.. .. .. .. .| .| .| .|
.o .o -o -o .o .o -o -o
where 4a(n-2) of these are not forests, namely the extensions of a(n-2) forests by 4 patterns:
.o-o -o-o .o-o -o-o
.| | .| | .| | .| |
.o-o .o-o -o-o -o-o (End)
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FORMULA
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G.f.: (2-x)/(1-8x+4x^2). - David Boyd and Ralf Stephan, Apr 15 2004
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MAPLE
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a:= n-> (Matrix([[15, 2]]). Matrix([[8, 1], [ -4, 0]])^n)[1, 2]: seq (a(n), n=0..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 18 2009]
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CROSSREFS
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Equals A028859(2n+2)/4.
Sequence in context: A062808 A162773 A140637 this_sequence A026113 A052874 A074622
Adjacent sequences: A022023 A022024 A022025 this_sequence A022027 A022028 A022029
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KEYWORD
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nonn
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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