A005910 Truncated octahedral numbers: 16*n^3 - 33*n^2 + 24*n - 6. (Formerly M5266)

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

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,changed

Author

N. J. A. Sloane

Extensions

Offset corrected by Daniel Forgues, Aug 15 2012

Status

approved