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A003600
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Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3 n^2 + 8 n)/6 (n>0).
(Formerly M1594)
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6
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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
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OFFSET
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0,2
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COMMENTS
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Both the bagel and the torus are solid! - N. J. A. Sloane, Oct 03 2012
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REFERENCES
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M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles and Diversions. Simon and Schuster, NY, 1961.
C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 373.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Torus Cutting.
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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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, Jan 11 2004
Binomial transform of [1, 1, 3, 0, 1, -1, 1, -1, 1,...]. - Gary W. Adamson, Nov 08 2007
G.f.: (1-2*x+4*x^2-3*x^3+x^4)/(1-x)^4. - Colin Barker, Jun 28 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012
a(n) = A108561(n+4,3) for n>0. - Reinhard Zumkeller, Jun 10 2005
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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 Joseph Stephan Orlovsky, May 24 2009]
CoefficientList[Series[(1-2*x+4*x^2-3*x^3+x^4)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *)
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PROG
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(MAGMA) I:=[1, 2, 6, 13, 24]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012
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CROSSREFS
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Cf. A000124 (slicing a pancake), A000125 (a cake).
Cf. A004148.
Sequence in context: A011891 A184533 A178532 * A000135 A065220 A048094
Adjacent sequences: A003597 A003598 A003599 * 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, Mira Bernstein
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EXTENSIONS
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More terms from James A. Sellers, Aug 22 2000
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STATUS
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approved
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