OFFSET
0,3
COMMENTS
3-dimensional analog of centered polygonal numbers.
(1), (4+7), (10+13+16), (19+22+25+28), ... - Jon Perry, Sep 10 2004
REFERENCES
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140.
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Partial sums of n-1 3-spaced triangular numbers, e.g., a(4) = t(1) + t(4) + t(7) = 1 + 10 + 28 = 39. - Jon Perry, Jul 23 2003
a(n) = C(2*n+1,3) + C(n+1,3), n >= 0. - Zerinvary Lajos, Jan 21 2007
G.f.: x*(1+7*x+x^2) / (x-1)^4. - R. J. Mathar, Oct 08 2011
From Miquel Cerda, Dec 25 2016: (Start)
E.g.f.: (x/2)*(2 + 9*x + 3*x^2)*exp(x). - G. C. Greubel, Sep 01 2017
MAPLE
seq(binomial(2*n+1, 3)+binomial(n+1, 3), n=0..37); # Zerinvary Lajos, Jan 21 2007
MATHEMATICA
Table[n(3n^2-1)/2, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 11, 39}, 40] (* Harvey P. Dale, Jul 19 2019 *)
PROG
(PARI) vector(40, n, n*(3*n^2-1)/2)
(Magma) [n*(3*n^2-1)/2: n in [0..50]]; //Vincenzo Librandi, May 15 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Albert D. Rich (Albert_Rich(AT)msn.com)
STATUS
approved