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A063843 Number of n-multigraphs on 5 nodes. 11
0, 1, 34, 792, 10688, 90005, 533358, 2437848, 9156288, 29522961, 84293770, 217993600, 519341472, 1154658869, 2420188694, 4821091920, 9187076352, 16837177281, 29809183410, 51172613512, 85448030080, 139159855989, 221554769150, 345523218536, 528767663040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equivalently, number of ways to color edges of complete graph on 5 nodes with n colors, under action of symmetric group S_5, of order 120, with cycle index on edges given by (1/120)*(24*x5^2 + 30*x2*x4^2 + 20*x3^3*x1 + 20*x3*x6*x1 + 15*x1^2*x2^4 + 10*x1^4*x2^3 + x1^10). Setting all x_i = n gives the sequence.

Number of vertex colorings of the Petersen graph. Marko Riedel, Mar 24 2016

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes

Marko Riedel, Vertex colorings of the Petersen graph, Math StackExchange

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(n) = (1/120)*(24*n^2+50*n^3+20*n^4+15*n^6+10*n^7+n^10).

a(n+1) = (1/5!)*(n^10 + 10*n^9 + 45*n^8 + 130*n^7 + 295*n^6 + 552*n^5 + 805*n^4 + 900*n^3 + 774*n^2 + 448*n + 120).

G.f. = (1 + 23*x + 473*x^2 + 3681*x^3 + 10717*x^4 + 11221*x^5 + 3779*x^6 + 339*x^7 + 6*x^8)/(1-x)^11.  - M. F. Hasler, Jan 19 2012

a(0)=0, a(1)=1, a(2)=34, a(3)=792, a(4)=10688, a(5)=90005, a(6)=533358, a(7)=2437848, a(8)=9156288, a(9)=29522961, a(10)=84293770, a(n)= 11*a(n-1)- 55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+ 330*a(n-7)- 165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). - Harvey P. Dale, Oct 20 2012

MAPLE

f:=n-> 1/120*(24*n^2+50*n^3+20*n^4+15*n^6+10*n^7+n^10);

MATHEMATICA

Table[(24n^2+50n^3+20n^4+15n^6+10n^7+n^10)/120, {n, 0, 30}] (* or *) LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 1, 34, 792, 10688, 90005, 533358, 2437848, 9156288, 29522961, 84293770}, 30] (* Harvey P. Dale, Oct 20 2012 *)

PROG

(PARI) a(n)=n^2*(n^8+10*n^5+15*n^4+20*n^2+50*n+24)/120 \\ Charles R Greathouse IV, Jan 20 2012

CROSSREFS

Cf. A063842. A row of A063841.

Sequence in context: A025190 A160315 A078193 * A192094 A297337 A295351

Adjacent sequences:  A063840 A063841 A063842 * A063844 A063845 A063846

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 25 2001

EXTENSIONS

More terms from Vladeta Jovovic, Sep 02 2001

STATUS

approved

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Last modified May 23 05:03 EDT 2019. Contains 323508 sequences. (Running on oeis4.)