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Search: id:A162485
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| A162485 |
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a(1) = 4, a(2) = 6; a(n) = 2 a(n - 1) + a(n - 2) - 4 Mod[n - 1, 2] |
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+0
1
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| 4, 6, 16, 34, 84, 198, 480, 1154, 2788, 6726, 16240, 39202, 94644, 228486, 551616, 1331714, 3215044, 7761798, 18738640, 45239074, 109216788, 263672646, 636562080, 1536796802, 3710155684
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is the number of perfect matchings of an edge-labeled 2 x n Klein bottle grid graph, or equivalently the number of domino tilings of a 2 x n Klein bottle grid. (The twist is on the length-2 side.)
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REFERENCES
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S.-M. Belcastro, Tilings of 2 x n Grids on Surfaces, preprint.
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FORMULA
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for n > 1, 1/2 ((1 + Sqrt[2])^n (2 + (-1 + Sqrt[2])^(2 Floor[1/2 (-1 + n)]) (-4 + 3 Sqrt[2])) + (1 - Sqrt[2])^n (2 - (-1 - Sqrt[2])^(2 Floor[1/2 (-1 + n)]) (4 + 3 Sqrt[2])))
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EXAMPLE
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a(3) = 2 a(2) + a(1) - 4 Mod[2,2] = 2*6 + 4 - 0 = 16
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CROSSREFS
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Sequence in context: A099430 A113883 A036748 this_sequence A076066 A165799 A056421
Adjacent sequences: A162482 A162483 A162484 this_sequence A162486 A162487 A162488
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KEYWORD
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easy,nonn
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AUTHOR
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Sarah-Marie Belcastro (smbelcas(AT)toroidalsnark.net), Jul 04 2009
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