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Search: id:A028447
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| A028447 |
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Number of perfect matchings in graph P_{2} X P_{3} X P_{n}. |
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+0
1
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| 3, 32, 229, 1845, 14320, 112485, 880163, 6895792, 54003765, 422983905, 3312866080, 25947198337, 203223953179, 1591695681488, 12466511517581, 97640484615909, 764741896529104, 5989627994067061, 46912093390144139
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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lim(a(n)^(1/n), n -> infinity) = 7.832221... - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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REFERENCES
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Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.
H. Narumi and H. Hosoya, Generalized expression of the perfect matching number of 2 X 3 X n lattices, J. Math. Phys. 34 (3), 1993, 1043-1051.
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LINKS
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Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
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FORMULA
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a(n) = 6a(n - 1) + 21a(n - 2) - 42a(n - 3) - 89a(n - 4) + 68a(n - 5) + 89a(n - 6) - 42a(n - 7) - 21a(n - 8) + 6a(n - 9) + a(n - 10). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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MAPLE
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a[0]:=1: a[1]:=3: a[2]:=32: a[3]:=229: a[4]:=1845: a[5]:=14320: a[6]:=112485: a[7]:=880163: a[8]:=6895792: a[9]:=54003765: a[10]:=422983905: for n from 11 to 20 do a[n]:=6*a[n-1]+21*a[n-2]-42*a[n-3]-89*a[n-4]+68*a[n-5]+89*a[n-6]-42*a[n-7]-21*a[\ n-8]+6*a[n-9]+a[n-10] od: seq(a[n], n=1..19); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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CROSSREFS
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Sequence in context: A119940 A004256 A002059 this_sequence A081012 A035533 A029502
Adjacent sequences: A028444 A028445 A028446 this_sequence A028448 A028449 A028450
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KEYWORD
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nonn
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AUTHOR
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Per Hakan Lundow (phl(AT)theophys.kth.se)
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