OFFSET
0,2
COMMENTS
a(n-1) is the number of unoriented ways to color the edges of a regular tetrahedron with up to n colors.
LINKS
Vincenzo Librandi, 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 R. Riedel, Counting multigraphs up to isomorphism
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = (1/4!)*(n^6 + 6*n^5 + 24*n^4 + 56*n^3 + 83*n^2 + 70*n + 24).
G.f.: (1 + 3*x + 7*x^2 + 3*x^3 + x^4)*(1+x)/(1-x)^7. - M. F. Hasler, Jan 19 2012
MATHEMATICA
Needs["Combinatorica`"]
Table[Total[Table[CycleIndex[KSubsetGroup[GraphData[{4, k}, "Automorphisms"], GraphData[{4, k}, "EdgeIndices"]], s], {k, 1, 11}]]/.Table[s[i] -> n, {i, 1, 4}], {n, 0, 30}] (* Geoffrey Critzer, Oct 22 2012 *)
CoefficientList[Series[(1 + 3 x + 7 x^2 + 3 x^3 + x^4) (1 + x) / (1 - x)^7, {x, 0, 35}], x] (* Vincenzo Librandi, Jul 21 2013 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 11, 66, 276, 900, 2451, 5831}, 40] (* Harvey P. Dale, Sep 10 2023 *)
PROG
(Magma) [1/24*(n^6+6*n^5+24*n^4+56*n^3+83*n^2+70*n+24): n in [0..35]]; // Vincenzo Librandi, Jul 21 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 25 2001
EXTENSIONS
More terms from Vladeta Jovovic, Sep 02 2001
STATUS
approved