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A003600 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)
7
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Both the bagel and the torus are solid! - N. J. A. Sloane, Oct 03 2012

REFERENCES

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).

LINKS

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).

FORMULA

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from James A. Sellers, Aug 22 2000

STATUS

approved

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Last modified November 24 12:07 EST 2014. Contains 249898 sequences.