A160457 a(n) = n^2 - 2*n + 2.

2, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 325, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1297, 1370, 1445, 1522, 1601, 1682, 1765, 1850, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810

Offset: 0

Author

Jonathan Vos Post, May 14 2009

Keywords

• easy
• nonn

Comments

Competition number of the complete bipartite graph K_{n,n}.

Formula given on p. 3 of Sano's article.

Links

• Yoshio Sano, The competition numbers of regular polyhedra, arXiv:0905.1763 [math.CO], 2009.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A002378, A002522, A160450.

Programs

Mathematica

Table[n^2-2*n+2, {n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Dec 29 2010 *)
LinearRecurrence[{3,-3,1},{2,1,2},60] (* Harvey P. Dale, Mar 29 2015 *)

PARI

vector(100,n,n--;n^2 - 2*n + 2)

Formula

a(n) = a(n-1) + 2*n - 3 (with a(0)=2). - Vincenzo Librandi, Dec 03 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: (2 - 5*x + 5*x^2)/(1-x)^3.

a(n) = A002522(n-1). - Michel Marcus, Feb 03 2016

a(n) = (1/4)*(A002378(n) + A002378(n-1) + A002378(n-2) + A002378(n-3)). - Peter Bala, Jun 11 2024

E.g.f.: exp(x)*(2 - x + x^2). - Elmo R. Oliveira, Nov 13 2024

Extensions

More terms from Vincenzo Librandi, Nov 08 2009

Sequence corrected by Joerg Arndt, Dec 03 2010