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 A005910 Truncated octahedral numbers: 16*n^3 - 33*n^2 + 24*n - 6. (Formerly M5266) 3
 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; text; internal format)
 OFFSET 1,2 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. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 (offset corrected by Daniel Forgues, Aug 16 2012). T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (7). B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558. Eric Weisstein's World of Mathematics, Truncated Octahedral Number Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA 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 MAPLE A005910:=n->16*n^3-33*n^2+24*n-6: seq(A005910(n), n=1..60); # Wesley Ivan Hurt, Nov 04 2017 MATHEMATICA 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 *) PROG (PARI) a(n)=16*n^3-33*n^2+24*n-6 \\ Charles R Greathouse IV, May 29 2011 (Magma) [16*n^3-33*n^2+24*n-6: n in [1..41]]; // Vincenzo Librandi, May 30 2011 CROSSREFS Sequence in context: A160064 A297541 A235079 * A281769 A191698 A124238 Adjacent sequences: A005907 A005908 A005909 * A005911 A005912 A005913 KEYWORD nonn,easy AUTHOR EXTENSIONS Offset corrected by Daniel Forgues, Aug 15 2012 STATUS approved

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Last modified December 2 18:40 EST 2022. Contains 358510 sequences. (Running on oeis4.)