OFFSET
1,2
COMMENTS
For n>2, maximal number of edges in critical strongly connected digraphs on n-1 vertices.
If Y is a 3-subset of an n-set X then, for n>=3, a(n) is the number of 2-subsets of X which do not have exactly one element in common with Y. Also, if Y is a 3-subset of an n-set X then, for n>=4, a(n-3) is the number of (n-2)-subsets of X which have no exactly two elements in common with Y. - Milan Janjic, Dec 28 2007
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
R. Aharoni and E. Berger, The number of edges in critical strongly connected graphs, arXiv:math/9911113 [math.CO], 1999.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
Also, from the third term on, triangular numbers + 3. - Alexandre Wajnberg, Dec 10 2005
a(n) = binomial(n,2) - 3*n + 9, n>=3. a(n-3) = n^2/2 - 7*n/2 + 9, n>=4. - Milan Janjic, Dec 28 2007
MATHEMATICA
i=0; s=3; lst={1, 2}; Do[s+=n+i; AppendTo[lst, s], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 30 2008 *)
CoefficientList[Series[(1-x+x^4)/(1-x)^3, {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 3, 4, 6}, 60] (* Harvey P. Dale, Nov 30 2015 *)
PROG
(PARI) Vec((1-x+x^4)/(1-x)^3+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition corrected by Harvey P. Dale, Nov 30 2015
STATUS
approved