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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

Magma

[16*n^3-33*n^2+24*n-6: n in [1..41]]; // Vincenzo Librandi, May 30 2011

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 *)

PARI

a(n)=16*n^3-33*n^2+24*n-6 \\ Charles R Greathouse IV, May 29 2011

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

Extensions

Offset corrected by Daniel Forgues, Aug 15 2012