0,3

Number of edges in the line graph of the complete bipartite graph of order 2n, L(K_n,n) - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002

Number of edges of the product of two complete graphs, each of order n, K_n x K_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002

n such that x^3 + x^2 + n factors over the integers. - James Buddenhagen (jbuddenh(AT)gmail.com), Apr 19 2005

Also the number of triangles in a 2 X n grid of points and therefore also (n choose 2) * (n choose 1) * 2, or (2n choose 3) - 2*(n choose 3). - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jan 11 2006

Sequence allows us to find X values of the equation: (X-Y)^3-XY=0. To find Y values: b(n)=(n+1)*n^2 (see A011379). I proved that if(X,Y) is different from (0,0) and m=2,4,6,8,10,12,...than the equation (X-Y)^m-XY=0,... has no solution. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 10 2006

For n>=1, a(n) is equal to the number of functions f:{1,2,3}->{1,2,...,n} such that for a fixed x in {1,2,3} and a fixed y in {1,2,...,n} we have f(x)<>y. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 13 2007

Number of units of a(n) belongs to a periodic sequence: 0, 0, 4, 8, 8. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 04 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

R. J. Mathar, On the Diophantine equation (X-Y)^m-XY=0 (PDF).

a(n)=sum(sum(n, j=2..n),k=1..n): n>=0. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007

G.f.: 2*x^2*(x+2)/(-1+x)^4 = 6/(-1+x)^4+10/(-1+x)^2+14/(-1+x)^3+2/(-1+x). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2007

a:=n->sum(numbperm (n, 2), j=1..n): seq(a(n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007

a:=n->sum(sum(n, j=2..n), k=1..n): seq(a(n), n=0..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007

a:=n->sum(sum(sum(1, j=1..n), k=0..n), m=0..n): seq(a(n), n=-1..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007

a[n_]:=n^3-n^2; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 22 2008]

(Other) sage: [n^2*(n-1) for n in xrange(0, 40)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2009]

Cf. A047929.

Cf. A011379.

Sequence in context: A066153 A023650 A163188 this_sequence A114364 A027271 A073991

Adjacent sequences: A045988 A045989 A045990 this_sequence A045992 A045993 A045994

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).