The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054981 Number of certain connected weighted pseudo-graphs. 1
 1, 2, 8, 14, 57, 161, 680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of connected graphs, multi-edges and self-loops allowed, of weight n with vertices (nodes) of degree 1, 3 or 4 only. The weight of a 1-, 3-, 4-vertex is 0,1,2, respectively. Number of edges: e = (V1+3*V3+4*V4)/2 = (3*n+V1-2*V4)/2; cyclomatic number c = 1-V+e = (n-V1+2)/2; where Vi is the number of i-vertices, i=1,3,4, V= V1+V3+V4 and n = V3+2*V4 is the weight. REFERENCES E. Vargas, The SU(2)xU(1)xU(1) Extension of the Electroweak Standard Model, PhD thesis, Karlsruhe University, 2000, tbp, (for n >= 1). LINKS Sean A. Irvine, Initial Terms of A054981 Sean A. Irvine, Java program (github) EXAMPLE n=0: V1=2, e=1, f=1; n=1: V3=1, V1=3, e=3, c=0; n=2: V3=1, V1=1, e=2, c=1; n=3: ... CROSSREFS Sequence in context: A055258 A277649 A192777 * A059449 A272930 A140973 Adjacent sequences:  A054978 A054979 A054980 * A054982 A054983 A054984 KEYWORD nonn,more AUTHOR Edwin Vargas (edwin.vargas@gmx.de), May 30 2000 EXTENSIONS a(5)-a(6) from Sean A. Irvine, Mar 07 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)