A004467 a(n) = n*(11*n^2 - 5)/6.

0, 1, 13, 47, 114, 225, 391, 623, 932, 1329, 1825, 2431, 3158, 4017, 5019, 6175, 7496, 8993, 10677, 12559, 14650, 16961, 19503, 22287, 25324, 28625, 32201, 36063, 40222, 44689, 49475, 54591, 60048

Offset: 0

Author

Albert D. Rich (Albert_Rich(AT)msn.com)

Keywords

• nonn
• easy

Comments

3-dimensional analog of centered polygonal numbers, that is: centered hendecagonal pyramidal numbers (see Deza paper in References).

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Crossrefs

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.

Programs

Magma

[n*(11*n^2-5)/6: n in [0..50]]; // Vincenzo Librandi, May 15 2011

Mathematica

Table[n(11n^2-5)/6,{n,0,80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
LinearRecurrence[{4,-6,4,-1},{0,1,13,47},80] (* Harvey P. Dale, Sep 22 2013 *)

PARI

a(n)=n*(11*n^2-5)/6 \\ Charles R Greathouse IV, Sep 28 2011

Formula

G.f.: x*(1+9*x+x^2)/(1-x)^4. - Colin Barker, Jan 08 2012

a(0)=0, a(1)=1, a(2)=13, a(3)=47; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Sep 22 2013

E.g.f.: (x/6)*(6 + 33*x + 11*x^2)*exp(x). - G. C. Greubel, Sep 01 2017