Search: id:A006011
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%I A006011 M3044
%S A006011 0,0,3,18,60,150,315,588,1008,1620,2475,3630,5148,7098,9555,12600,16320,
%T A006011 20808,26163,32490,39900,48510,58443,69828,82800,97500,114075,132678,
%U A006011 153468,176610,202275,230640,261888,296208,333795,374850,419580,468198
%N A006011 n^2*(n^2-1)/4.
%C A006011 Products of two consecutive triangular numbers (A000217).
%C A006011 a(n) = number of Lyndon words of length 4 on an n-letter alphabet. A 
               Lyndon word is a primitive word that is lexicographically smallest 
               in its cyclic rotation class. For example, a(2)=3 counts 1112, 1122, 
               1222. - David Callan (callan(AT)stat.wisc.edu), Nov 29 2007
%D A006011 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006011 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, 
               Chem. Ber. 30 (1897), 1917-1926.
%H A006011 M. Azaola and F. Santos, <a href="http://personales.unican.es/santosf/
               Articulos/">The number of triangulations of the cyclic polytope C(n,
               n-4)</a>, Discrete Comput. Geom., 27 (2002), 29-48 (see Prop. 4.2(a)).
%F A006011 G.f.: 3*(1 + x ) / ( 1 - x )^5.
%F A006011 a(n) = (n-1)n/2 * n(n+1)/2 = A000217(n-1)*A000217(n) = 1/2*(n^2-1)*n^2/
               2 = 1/2*A000217(n^2-1). - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Apr 13 2006
%F A006011 a(n) = 3*A002415(n) = A047928(n-1)/4 = A083374(n-1)/2 = A008911(n)*3/
               2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
%p A006011 [seq((binomial(3+n,2)-binomial(2+n,1))*(binomial(4+n,3)-binomial(3+n,
               3)),n=-2..39)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               May 29 2006
%p A006011 [seq (stirling2(n+1,n)*binomial(n,2),n=0..37)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 05 2006
%p A006011 a:=n->sum(k^3+sum(k, k=0..n), k=0..n):seq(a(n), n=-1...36); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 01 2008
%p A006011 a:=n->sum(k^3+sum(k, k=0..n), k=0..n):seq(a(n), n=-1...36); [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Aug 09 2008]
%t A006011 Table[ n^2*(n^2 - 1)/4, {n, 0, 38} ]
%Y A006011 Thrice A002415. Row 4 of A074650.
%Y A006011 Cf. A002415, A008911, A047928, A083374.
%Y A006011 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 
               2009: (Start)
%Y A006011 Equals for n=>2 second right hand column of A163932.
%Y A006011 (End)
%Y A006011 Sequence in context: A061317 A139362 A012763 this_sequence A012779 A074439 
               A000648
%Y A006011 Adjacent sequences: A006008 A006009 A006010 this_sequence A006012 A006013 
               A006014
%K A006011 nonn,easy
%O A006011 0,3
%A A006011 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A006011 More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 
               2006

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