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Search: id:A002889
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| A002889 |
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Arrays of dumbbells.
(Formerly M4715 N2016)
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+0
10
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| 1, 10, 56, 234, 815, 2504, 7018, 18336, 45328, 107160, 244198, 539656, 1161987, 2446906, 5054440, 10266850, 20549117, 40595568, 79271188, 153190480, 293278496, 556737696, 1048772300, 1961855408, 3646420325, 6737649754
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
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FORMULA
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a(n)=2*a(n-1)-a(n-3)+A002941(n)+A002941(n-1)
G.f.: (1+x)^3/(1-x-x^2)^4/(1-x)^3.
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CROSSREFS
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Cf. A046741, A002940, A002941.
Cf. A055608, A062123-A062127.
Sequence in context: A001786 A053309 A035040 this_sequence A055911 A014483 A087076
Adjacent sequences: A002886 A002887 A002888 this_sequence A002890 A002891 A002892
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), Jun 02 2000
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