A090491 G.f.: (1+x^3+x^4+x^5+x^6+x^9)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^4)).

1, 1, 3, 5, 10, 15, 26, 37, 57, 79, 112, 149, 202, 260, 338, 425, 536, 659, 812, 980, 1184, 1408, 1673, 1963, 2302, 2670, 3094, 3554, 4077, 4642, 5279, 5964, 6730, 7552, 8463, 9438, 10513, 11659, 12915, 14252, 15709, 17256, 18935, 20713, 22635, 24667, 26854

Offset

0,3

Comments

Molien series for permutation representation of S_4 on pairs of elements from a set of size 4.

References

H. Derksen and G. Kemper, Computational Invariant Theory, Springer, 2002; p. 92.

Links

Table of n, a(n) for n=0..46.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,-2,2,0,1,0,-2,1).

Formula

G.f.: ( -1+x-x^2-x^6+x^7-x^8-x^4 ) / ( (1+x+x^2)*(x^2+1)*(1+x)^2*(x-1)^5 ). - R. J. Mathar, Dec 18 2014

a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11) for n>10. - Harvey P. Dale, Apr 10 2015

Mathematica

CoefficientList[Series[(1+x^3+x^4+x^5+x^6+x^9)/((1-x)(1-x^2)^2(1-x^3)(1-x^4)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 0, -1, 0, -2, 2, 0, 1, 0, -2, 1}, {1, 1, 3, 5, 10, 15, 26, 37, 57, 79, 112}, 50] (* Harvey P. Dale, Apr 10 2015 *)

Crossrefs

Sequence in context: A238620 A074968 A308826 * A126728 A070557 A225751

Adjacent sequences: A090488 A090489 A090490 * A090492 A090493 A090494

Keyword

nonn

Author

N. J. A. Sloane, Feb 02 2004

Status

approved