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A005910
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Truncated octahedral numbers: 16*n^3 - 33*n^2 + 24*n - 6.
(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;
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refs;
listen;
history;
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OFFSET
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1,2
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REFERENCES
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (7).
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FORMULA
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G.f.: x*(6*x^3 + 55*x^2 + 34*x + 1)/(1-x)^4.
E.g.f.: 6 + (-6 + 7*x + 15*x^2 + 16*x^3)*exp(x). - G. C. Greubel, Nov 04 2017
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MAPLE
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MATHEMATICA
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Table[16n^3-33n^2+24n-6, {n, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 38, 201, 586}, 50] (* Harvey P. Dale, Jun 01 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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