0,3

Also as a(n)=(1/6)*(12*n^3-6*n), n>0: structured hexagonal anti-diamond numbers (vertex structure 13) (Cf. A005915 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov. 7, 2004.

The only known square stella octangula number for n>1 is a(169) = 169*(2*169^2 - 1) = 9653449 = 3107^2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 51.

T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).

Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2008, Table of n, a(n) for n = 0..169

Index entries for sequences related to linear recurrences with constant coefficients

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

G.f.: (x+10*x^2+x^3)/(1-x)^4.

Table[ n(2n^2-1), {n, 0, 169} ] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2008

(PARI) a(n)=n*(2*n^2-1)

Backwards differences give star numbers A003154: A003154(n)=A007588(n)-A007588(n-1).

1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.

Cf. A001653 = Numbers n such that 2*n^2 - 1 is a square.

Adjacent sequences: A007585 A007586 A007587 this_sequence A007589 A007590 A007591

Sequence in context: A043912 A009961 A059997 this_sequence A129025 A113907 A125740

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

In the formula given in the 1995 Encyclopedia of Integer Sequences, the second 2 should be an exponent.