Search: id:A003600
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%I A003600 M1594
%S A003600 1,2,6,13,24,40,62,91,128,174,230,297,376,468,574,695,832,986,1158,
%T A003600 1349,1560,1792,2046,2323,2624,2950,3302,3681,4088,4524,4990,5487,6016,
%U A003600 6578,7174,7805,8472,9176,9918,10699,11520,12382,13286,14233,15224
%N A003600 Slicing a torus with n cuts: (n^3 + 3 n^2 + 8 n)/6 (n>0).
%C A003600 a(n) = A108561(n+4,3) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 10 2005
%D A003600 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003600 C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, 
               p. 373.
%D A003600 M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles 
               and Diversions. Simon and Schuster, NY, 1961.
%H A003600 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TorusCutting.html">Link to a section of The World of Mathematics.</
               a>
%F A003600 a(n)=binomial(n+2, n-1)+binomial(n, n-1).
%F A003600 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
%F A003600 Binomial transform of [1, 1, 3, 0, 1, -1, 1, -1, 1,...]. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Nov 08 2007
%t A003600 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]
%Y A003600 Cf. A000124, A000125.
%Y A003600 Cf. A004148.
%Y A003600 Sequence in context: A064960 A143689 A011891 this_sequence A000135 A065220 
               A048094
%Y A003600 Adjacent sequences: A003597 A003598 A003599 this_sequence A003601 A003602 
               A003603
%K A003600 nonn,easy,nice
%O A003600 0,2
%A A003600 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
%E A003600 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 22 2000

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