|
Search: id:A058831
|
|
|
| A058831 |
|
Number of labeled n-node 4-valent graphs containing two nonadjacent double edges. |
|
+0
9
|
|
| 0, 0, 0, 0, 3, 30, 405, 10080, 369180, 17959158, 1092909510, 81043601760, 7195434965235, 753877707936210, 92048844661576803, 12957249486666966390, 2083048648390795634640, 379312444955136162744540
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
In Table I of the Read-Wormald paper the c and d rows actually show double the numbers (Wormald). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2005
|
|
REFERENCES
|
R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.
|
|
FORMULA
|
Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2005
|
|
MAPLE
|
a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(c[n], n=0..20); # A058831(n)=c[n] (Deutsch)
|
|
CROSSREFS
|
Cf. A005815, A058830, A058832, A058833, A058834, A058835, A058836, A058837.
Sequence in context: A037771 A037659 A131586 this_sequence A007004 A012003 A064352
Adjacent sequences: A058828 A058829 A058830 this_sequence A058832 A058833 A058834
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
njas, Jan 05 2001
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2005
|
|
|
Search completed in 0.002 seconds
|
