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Search: id:A005906
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| A005906 |
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Truncated tetrahedral numbers: (1/6)*(n+1)*(23*n^2+19*n+6).
(Formerly M5002)
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+0
3
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| 1, 16, 68, 180, 375, 676, 1106, 1688, 2445, 3400, 4576, 5996, 7683, 9660, 11950, 14576, 17561, 20928, 24700, 28900, 33551, 38676, 44298, 50440, 57125, 64376, 72216, 80668, 89755, 99500, 109926, 121056, 132913, 145520, 158900, 173076
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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.
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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LINKS
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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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=binomial(3*n, 3)-4*binomial(n+1, 3)=1/6*n*(23*n^2-27*n+10)
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MAPLE
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A005906:=(1+12*z+10*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A039330 A043933 A100186 this_sequence A036660 A063493 A027997
Adjacent sequences: A005903 A005904 A005905 this_sequence A005907 A005908 A005909
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 20 1999
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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