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A005910
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Truncated octahedral numbers: 16*n^3+15*n^2+6*n+1.
(Formerly M5266)
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3
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1, 38, 201, 586, 1289, 2406, 4033, 6266, 9201, 12934, 17561, 23178, 29881, 37766, 46929, 57466, 69473, 83046, 98281, 115274, 134121, 154918, 177761, 202746, 229969, 259526, 291513, 326026, 363161, 403014, 445681, 491258
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 52
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.
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (7).
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
| Vincenzo Librandi, Table of n, a(n) for n = 0..2000
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, Truncated Octahedral Number
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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MAPLE
| A005910:=(1+34*z+55*z**2+6*z**3)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROG
| (PARI) a(n)=16*n^3+15*n^2+6*n+1 \\ Charles R Greathouse IV, May 29 2011
(MAGMA) [16*n^3+15*n^2+6*n+1: n in [0..40]]; // Vincenzo Librandi, May 30 2011
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CROSSREFS
| Sequence in context: A100168 A137022 A160064 * A191698 A124238 A020870
Adjacent sequences: A005907 A005908 A005909 * A005911 A005912 A005913
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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