|
| |
|
|
A152743
|
|
6 times pentagonal numbers: 3n(3n-1).
|
|
8
|
|
|
|
0, 6, 30, 72, 132, 210, 306, 420, 552, 702, 870, 1056, 1260, 1482, 1722, 1980, 2256, 2550, 2862, 3192, 3540, 3906, 4290, 4692, 5112, 5550, 6006, 6480, 6972, 7482, 8010, 8556, 9120, 9702, 10302, 10920, 11556, 12210, 12882, 13572, 14280
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Contribution from Emeric Deutsch, Sep 21 2010: (Start)
a(n) is also the Wiener index of the windmill graph D(4,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e. a bouquet of n pieces of K_m graphs). The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph. The Wiener index of D(m,n) is (1/2)n(m-1)[(m-1)(2n-1)+1]. For the Wiener indices of D(3,n), D(5,n), and D(6,n) see A033991, A028994, and A180577, respectively.
(End)
|
|
|
LINKS
|
Table of n, a(n) for n=0..40.
Eric Weisstein's World of Mathematics, Windmill Graph [From Emeric Deutsch, Sep 21 2010]
|
|
|
FORMULA
|
a(n) = 9n^2 - 3n = A000326(n)*6.
a(n) = A049450(n)*3 = A062741(n)*2. [From Omar E. Pol, Dec 15 2008]
a(n)=a(n-1)+18*n-12 (with a(0)=0) [From Vincenzo Librandi, Nov 26 2010]
G.f.: -((6*x*(2*x+1))/(x-1)^3) [From Harvey P. Dale, June 30 2011]
|
|
|
MATHEMATICA
|
s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 6, 7!, 18}]; lst [From Vladimir Joseph Stephan Orlovsky, Apr 03 2009]
Table[3n(3n-1), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 6, 30}, 40] (* From Harvey P. Dale, June 30 2011 *)
|
|
|
CROSSREFS
|
Cf. A000326, A152734, A152744.
Cf. A049450, A062741. [From Omar E. Pol, Dec 15 2008]
Cf. A033991, A028994, A180577 [From Emeric Deutsch, Sep 21 2010]
Sequence in context: A056836 A163640 A199130 * A215906 A038039 A050972
Adjacent sequences: A152740 A152741 A152742 * A152744 A152745 A152746
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Omar E. Pol, Dec 12 2008
|
|
|
EXTENSIONS
|
Converted reference to link by Omar E. Pol, Oct 07 2010
|
|
|
STATUS
|
approved
|
| |
|
|
