%I #14 Nov 21 2013 13:11:19
%S 4,8,12,20,24,32,40,52,60,72,84,100,112,128,144,164,180,200,220,244,
%T 264,288,312,340,364,392,420,452,480,512,544,580,612,648,684,724,760,
%U 800,840,884,924,968,1012,1060,1104,1152,1200,1252,1300,1352,1404,1460
%N Minimal number of vertices in 1-1 deficient regular graph where minimal degree is 1 and maximal degree is n.
%C A 1-1 deficient regular graph is one in which every vertex has the same degree as all of its neighbors except exactly one and its degree differs from the degree of this neighbor by exactly 1.
%H Vincenzo Librandi, <a href="/A033691/b033691.txt">Table of n, a(n) for n = 2..1000</a>
%F a(2*i) = 2*i*(i+1) i=1, 2, 3, ...; a(4*i+3) = 2*(i+1)*(4*i+4) i=0, 1, 2, ...; a(4*i+5) = 4*(2*i^2+6*i+5) i=1, 2, 3, ...
%F Empirical G.f.: -4*x^2*(x^5-2*x^4+x^3+1) / ((x-1)^3*(x+1)*(x^2+1)). [_Colin Barker_, Jan 15 2013]
%t a[n_?EvenQ] := n*(n+2)/2; a[n_ /; Mod[n, 4] == 3] := (n+1)^2/2; a[n_ /; Mod[n, 4] == 1] := (n^2 + 2*n + 5)/2; Table[a[n], {n, 2, 53}] (* _Jean-François Alcover_, Oct 10 2011 *)
%K easy,nice,nonn
%O 2,1
%A Lisa R. Macon (lmacon(AT)valencia.cc.fl.us)
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003