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Search: id:A078469
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| A078469 |
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Number of different compositions of the ladder graph L_n. |
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+0
5
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| 1, 2, 12, 74, 456, 2810, 17316, 106706, 657552, 4052018, 24969660, 153869978, 948189528, 5843007146, 36006232404, 221880401570, 1367288641824, 8425612252514, 51920962156908, 319951385193962, 1971629273320680
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Comment from Hugo van der Sanden, Mar 23 2009: This is equally the number of partitions of a 2 x n rectangle into connected pieces consisting of unit squares cut along lattice lines, like a 2-d analogue of a partition into integers.
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REFERENCES
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J. N. Ridley and M. E. Mays, Compositions of unions of graphs, Fib. Quart. 42 (2004), 222-230.
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LINKS
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Tanya Khovanova, Recursive Sequences
A. Knopfmacher and M. E. Mays, Graph compositions,Integers 1(2001), #A04.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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a(n) = 6*a(n-1)+a(n-2). G.f.: 2*x/(1-6*x-x^2) (assumes a(0) = 0).
a(n) = ((3+s)^n-(3-s)^n)/s, where s = sqrt(10) (assumes a(0) = 0).
Asymptotic to (3+sqrt(10))^n/sqrt(10). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 03 2003
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CROSSREFS
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Cf. A108808, A110476. [From Brian Kell (s-bkell1(AT)math.unl.edu), Oct 21 2008]
Cf. A152113, A152124.
Sequence in context: A037718 A020049 A020004 this_sequence A014351 A074616 A006936
Adjacent sequences: A078466 A078467 A078468 this_sequence A078470 A078471 A078472
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 02 2003
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EXTENSIONS
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a(0) changed from 0 to 1 by N. J. A. Sloane, Sep 21 2009, at the suggesion of Hugo van der Sanden.
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