The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228695 Number of labeled graphs on 2n nodes with degree set {1,2,3}, with multiple edges and loops allowed. 2
1, 1, 7, 47, 521, 7233, 129443, 2811701, 73203561, 2229207953, 78389689559, 3138945552419, 141714151130833, 7146006410498833, 399443567886826899, 24581290495461129817, 1655664011866577666737, 121413069330848040859809, 9648772995329567310573319 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
I. P. Goulden and D. M. Jackson, Labelled graphs with small vertex degrees and P-recursiveness, SIAM J. Algebraic Discrete Methods 7(1986), no. 1, 60--66. MR0819706 (87k:05093).
FORMULA
See Goulden-Jackson for the e.g.f.
Recurrence (for n>9): 12*(3*n^4 - 19*n^3 + 19*n^2 + 24*n - 31)*a(n) = 6*(9*n^5 - 57*n^4 + 35*n^3 + 160*n^2 - 151*n - 4)*a(n-1) + 9*(n-1)*(3*n^6 - 25*n^5 + 61*n^4 - 16*n^3 - 135*n^2 + 104*n - 4)*a(n-2) + 3*(n-2)*(n-1)*(21*n^5 - 106*n^4 - 62*n^3 + 603*n^2 - 448*n - 6)*a(n-3) + 3*(n-3)*(n-2)*(n-1)*(21*n^5 - 106*n^4 + 15*n^3 + 208*n^2 - 209*n - 46)*a(n-4) + (n-4)*(n-3)*(n-2)*(n-1)*(51*n^4 - 77*n^3 - 526*n^2 + 477*n - 110)*a(n-5) - (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(9*n^5 - 42*n^4 - 29*n^3 + 159*n^2 - 120*n + 30)*a(n-6) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(6*n^4 - 14*n^3 - 11*n^2 + 22*n + 10)*a(n-7) + (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(3*n^4 - 7*n^3 - 20*n^2 + 17*n - 4)*a(n-8). - Vaclav Kotesovec, Sep 15 2014
MATHEMATICA
max=20; f[x_]:=Sum[a[n]*(x^(n)/n!), {n, 0, max}]; a[0]=1; a[1]=1; coef = CoefficientList[9*x^3*(x+2)*(x^3 - 2*x^2 + x - 1)*f''[x] - 3*(x^10 - 10*x^8 - 6*x^7 + 22*x^6 + 8*x^5 + 20*x^4 + 26*x^3 + 16*x - 8)*f'[x] + (x^11 - 2*x^10 - 14*x^9 + 24*x^8 + 74*x^7 - 61*x^6 - 99*x^5 - 55*x^4 - 180*x^3 - 48*x^2 - 96*x - 24)*f[x], x]; Table[a[n], {n, 0, max}]/.Solve[Thread[coef[[2;; max]]==0]][[1]] (* Vaclav Kotesovec, Sep 15 2014 *)
CROSSREFS
Sequence in context: A178002 A288722 A006873 * A368295 A268063 A015097
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 02 2013
EXTENSIONS
More terms from Vaclav Kotesovec, Sep 15 2014
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)