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Search: id:A003600
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| A003600 |
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Slicing a torus with n cuts: (n^3 + 3 n^2 + 8 n)/6 (n>0).
(Formerly M1594)
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+0
4
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| 1, 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, 297, 376, 468, 574, 695, 832, 986, 1158, 1349, 1560, 1792, 2046, 2323, 2624, 2950, 3302, 3681, 4088, 4524, 4990, 5487, 6016, 6578, 7174, 7805, 8472, 9176, 9918, 10699, 11520, 12382, 13286, 14233, 15224
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = A108561(n+4,3) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2005
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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).
C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 373.
M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles and Diversions. Simon and Schuster, NY, 1961.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=binomial(n+2, n-1)+binomial(n, n-1).
a(n)=coefficient of z^3 in the series expansion of G^n (n>0), where G=[1-z+z^2-sqrt(1-2z-z^2-2z^3+z^4)]/(2z^2) is the g.f. of A004148 (secondary structures of RNA molecules). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 11 2004
Binomial transform of [1, 1, 3, 0, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 08 2007
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MATHEMATICA
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a=2; s=3; lst={a, s}; Do[a+=n; s+=a; AppendTo[lst, s], {n, 2, 6!, 1}]; lst-1 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 24 2009]
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CROSSREFS
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Cf. A000124, A000125.
Cf. A004148.
Sequence in context: A064960 A143689 A011891 this_sequence A000135 A065220 A048094
Adjacent sequences: A003597 A003598 A003599 this_sequence A003601 A003602 A003603
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000
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