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%I M5266 #55 Sep 08 2022 08:44:34
%S 1,38,201,586,1289,2406,4033,6266,9201,12934,17561,23178,29881,37766,
%T 46929,57466,69473,83046,98281,115274,134121,154918,177761,202746,
%U 229969,259526,291513,326026,363161,403014,445681,491258
%N Truncated octahedral numbers: 16*n^3 - 33*n^2 + 24*n - 6.
%D J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 52
%D 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A005910/b005910.txt">Table of n, a(n) for n = 1..2000</a> (offset corrected by _Daniel Forgues_, Aug 16 2012).
%H T. P. Martin, <a href="http://dx.doi.org/10.1016/0370-1573(95)00083-6">Shells of atoms</a>, Phys. Reports, 273 (1996), 199-241, eq. (7).
%H B. K. Teo and N. J. A. Sloane, <a href="http://neilsloane.com/doc/magic1/magic1.html">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TruncatedOctahedralNumber.html">Truncated Octahedral Number</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: x*(6*x^3 + 55*x^2 + 34*x + 1)/(1-x)^4.
%F E.g.f.: 6 + (-6 + 7*x + 15*x^2 + 16*x^3)*exp(x). - _G. C. Greubel_, Nov 04 2017
%p A005910:=n->16*n^3-33*n^2+24*n-6: seq(A005910(n), n=1..60); # _Wesley Ivan Hurt_, Nov 04 2017
%t 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 *)
%o (PARI) a(n)=16*n^3-33*n^2+24*n-6 \\ _Charles R Greathouse IV_, May 29 2011
%o (Magma) [16*n^3-33*n^2+24*n-6: n in [1..41]]; // _Vincenzo Librandi_, May 30 2011
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E Offset corrected by _Daniel Forgues_, Aug 15 2012
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