The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A063843 Number of n-multigraphs on 5 nodes. 18
 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 Number of unoriented colorings of the 10 triangular edges or triangular faces of a pentachoron, SchlĂ¤fli symbol {3,3,3}, using n or fewer colors. Also called a 5-cell or 4-simplex. - Robert A. Russell, Oct 17 2020 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 From Robert A. Russell, Oct 17 2020: (Start) a(n) = A331350(n) - A331352(n) = (A331350(n) + A331353(n)) / 2 = A331352(n) + A331353(n). a(n) = 1*C(n,1) + 32*C(n,2) + 693*C(n,3) + 7720*C(n,4) + 44150*C(n,5) + 138312*C(n,6) + 247380*C(n,7) + 252000*C(n,8) + 136080*C(n,9) + 30240*C(n,10), where the coefficient of C(n,k) is the number of unoriented colorings using exactly k colors. (End) 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. Cf. A331350 (oriented), A331352 (chiral), A331353 (achiral), A000389(n+4) (vertices and facets), A331359 (tesseract edges, hyperoctahedron faces), A331355 (hyperoctahedron edges, tesseract faces). Row 4 of A327084 (simplex edges and ridges) and A337884 (simplex faces and peaks). 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

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

Last modified December 2 10:39 EST 2020. Contains 338876 sequences. (Running on oeis4.)