%I #36 Nov 13 2024 17:12:09
%S 2,1,2,5,10,17,26,37,50,65,82,101,122,145,170,197,226,257,290,325,362,
%T 401,442,485,530,577,626,677,730,785,842,901,962,1025,1090,1157,1226,
%U 1297,1370,1445,1522,1601,1682,1765,1850,1937,2026,2117,2210,2305,2402,2501,2602,2705,2810
%N a(n) = n^2 - 2*n + 2.
%C Competition number of the complete bipartite graph K_{n,n}.
%C Formula given on p. 3 of Sano's article.
%H Yoshio Sano, <a href="http://arxiv.org/abs/0905.1763">The competition numbers of regular polyhedra</a>, arXiv:0905.1763 [math.CO], 2009.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + 2*n - 3 (with a(0)=2). - _Vincenzo Librandi_, Dec 03 2010
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: (2 - 5*x + 5*x^2)/(1-x)^3.
%F a(n) = A002522(n-1). - _Michel Marcus_, Feb 03 2016
%F a(n) = (1/4)*(A002378(n) + A002378(n-1) + A002378(n-2) + A002378(n-3)). - _Peter Bala_, Jun 11 2024
%F E.g.f.: exp(x)*(2 - x + x^2). - _Elmo R. Oliveira_, Nov 13 2024
%t Table[n^2-2*n+2, {n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 29 2010 *)
%t LinearRecurrence[{3,-3,1},{2,1,2},60] (* _Harvey P. Dale_, Mar 29 2015 *)
%o (PARI) vector(100,n,n--;n^2 - 2*n + 2)
%Y Cf. A002378, A002522, A160450.
%K easy,nonn,changed
%O 0,1
%A _Jonathan Vos Post_, May 14 2009
%E More terms from _Vincenzo Librandi_, Nov 08 2009
%E Sequence corrected by _Joerg Arndt_, Dec 03 2010