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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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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
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OFFSET
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0,2
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COMMENTS
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A005906(n) is the number 4-element subsets of {-n,...,0,...n} having sum n. [From Clark Kimberling, Apr 05 2012]
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REFERENCES
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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Table of n, a(n) for n=0..35.
_Simon 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.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Truncated Tetrahedral Number.
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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 Simon Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A216306 A100186 A178574 * A211031 A200839 A036660
Adjacent sequences: A005903 A005904 A005905 * 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.
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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, Nov 07 2006
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STATUS
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approved
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