

A016028


Expansion of (1  x + x^4) / (1  x)^3.


3



1, 2, 3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, 949, 993, 1038, 1084, 1131, 1179
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

For n>2, maximal number of edges in critical strongly connected digraphs on n1 vertices.
If Y is a 3subset of an nset X then, for n>=3, a(n) is the number of 2subsets of X which have no exactly one element in common with Y. Also, if Y is a 3subset of an nset X then, for n>=4, a(n3) is the number of (n2)subsets of X which have no exactly two elements in common with Y.  Milan Janjic, Dec 28 2007


LINKS

Table of n, a(n) for n=1..51.
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(n3) = 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[(1x+x^4)/(1x)^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((1x+x^4)/(1x)^3+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012


CROSSREFS

Essentially triangular numbers (A000217) plus 3. Cf. A000124.
Sequence in context: A286929 A255525 A129632 * A239551 A219282 A098578
Adjacent sequences: A016025 A016026 A016027 * A016029 A016030 A016031


KEYWORD

nonn,easy


AUTHOR

Robert G. Wilson v


EXTENSIONS

Definition corrected by Harvey P. Dale, Nov 30 2015


STATUS

approved



