A033691 Minimal number of vertices in 1-1 deficient regular graph where minimal degree is 1 and maximal degree is n.

4, 8, 12, 20, 24, 32, 40, 52, 60, 72, 84, 100, 112, 128, 144, 164, 180, 200, 220, 244, 264, 288, 312, 340, 364, 392, 420, 452, 480, 512, 544, 580, 612, 648, 684, 724, 760, 800, 840, 884, 924, 968, 1012, 1060, 1104, 1152, 1200, 1252, 1300, 1352, 1404, 1460

Offset

2,1

Comments

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Formula

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, ...

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]

Mathematica

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 *)

Crossrefs

Sequence in context: A311655 A311656 A311657 * A090658 A268799 A359955

Adjacent sequences: A033688 A033689 A033690 * A033692 A033693 A033694

Keyword

easy,nice,nonn

Author

Lisa R. Macon (lmacon(AT)valencia.cc.fl.us)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003

Status

approved