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A005912
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Truncated cube numbers.
(Formerly M5312)
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2
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1, 56, 311, 920, 2037, 3816, 6411, 9976, 14665, 20632, 28031, 37016, 47741, 60360, 75027, 91896, 111121, 132856, 157255, 184472, 214661, 247976, 284571, 324600, 368217, 415576, 466831
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| 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
| 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.
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FORMULA
| a(n)=(3*n+1)^3-8*(n)*(n+1)*(n+2)/6=77/3*n^3+23*n^2+19/3*n+1
a(0)=1, a(1)=56, a(2)=311, a(3)=920, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4) [From Harvey P. Dale, Aug 14 2011]
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MAPLE
| A005912:=(1+52*z+93*z**2+8*z**3)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[(3n+1)^3-8(n)(n+1)(n+2)/6, {n, 0, 30}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 56, 311, 920}, 30] (* From Harvey P. Dale, Aug 14 2011 *)
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CROSSREFS
| Sequence in context: A205235 A205228 A110554 * A104677 A156375 A003783
Adjacent sequences: A005909 A005910 A005911 * A005913 A005914 A005915
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999
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