OFFSET
1,2
COMMENTS
Sum of two consecutive terms of A006003(n) = n*(n^2+1)/2. a(n) = A006003(n-1) + A006003(n). - Alexander Adamchuk, Jun 03 2006
If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-4) is the number of 5-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
Milan Janjic, Two Enumerative Functions
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
T. P. Martin, Shells of atoms, Phys. Rep., 273 (1996), 199-241, eq. (10).
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: (1 + x)*(1 + x + x^2)/(1 - x)^4. - Jaume Oliver Lafont, Aug 30 2009
E.g.f.: (-2 + 4*x + 3*x^2 + 2*x^3)*exp(x)/2 + 1. - G. C. Greubel, Dec 01 2017
MATHEMATICA
Table[(2 n - 1) (n^2 - n + 2)/2, {n, 1, 40}] (* Bruno Berselli, Oct 14 2016 *)
LinearRecurence[{4, -6, 4, -1}, {1, 6, 20, 49}, 50] (* G. C. Greubel, Dec 01 2017 *)
PROG
(PARI) { for (n=1, 1000, write("b063488.txt", n, " ", (2*n - 1)*(n^2 - n + 2)/2) ) } \\ Harry J. Smith, Aug 23 2009
(PARI) x='x+O('x^30); Vec(serlaplace((-2 + 4*x + 3*x^2 + 2*x^3)*exp(x)/2 + 1)) \\ G. C. Greubel, Dec 01 2017
(Magma) [(2*n-1)*(n^2 -n +2)/2: n in [1..30]]; // G. C. Greubel, Dec 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 01 2001
STATUS
approved