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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Offset corrected by Daniel Forgues, Aug 15 2012
STATUS
approved