Search: id:A005906
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%I A005906 M5002
%S A005906 1,16,68,180,375,676,1106,1688,2445,3400,4576,5996,7683,9660,11950,
%T A005906 14576,17561,20928,24700,28900,33551,38676,44298,50440,57125,64376,
%U A005906 72216,80668,89755,99500,109926,121056,132913,145520,158900,173076
%N A005906 Truncated tetrahedral numbers: (1/6)*(n+1)*(23*n^2+19*n+6).
%D A005906 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005906 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A005906 H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. 
               Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical 
               and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 
               1974.
%D A005906 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H A005906 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005906 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005906 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TruncatedTetrahedralNumber.html">Link to a section of The World of 
               Mathematics.</a>
%F A005906 a(n)=binomial(3*n, 3)-4*binomial(n+1, 3)=1/6*n*(23*n^2-27*n+10)
%p A005906 A005906:=(1+12*z+10*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%Y A005906 Sequence in context: A039330 A043933 A100186 this_sequence A036660 A063493 
               A027997
%Y A005906 Adjacent sequences: A005903 A005904 A005905 this_sequence A005907 A005908 
               A005909
%K A005906 nonn
%O A005906 0,2
%A A005906 N. J. A. Sloane (njas(AT)research.att.com).
%E A005906 More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), 
               Dec 20 1999
%E A005906 Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006

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