A055195 Number of 3-covers of an unlabeled n-set.

1, 9, 29, 72, 154, 294, 522, 877, 1406, 2172, 3255, 4746, 6763, 9445, 12953, 17480, 23254, 30528, 39604, 50823, 64568, 81276, 101443, 125610, 154395, 188479, 228611, 275622, 330432, 394032, 467524, 552103, 649064, 759818, 885901

Offset: 2

Author

Vladeta Jovovic, Jun 30 2000

Keywords

• nonn
• easy

Comments

Covers are defined in proper sense, i.e. without empty sets or multiple sets.

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Covers
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,-1,3,6,-6,-3,1,3,1,-3,1).

Crossrefs

Column 3 of A055130.

Cf. A005783.

Programs

Mathematica

Drop[CoefficientList[Series[x^2(x^11-x^10-3x^9+4x^7+6x^6-3x^5-5x^4-3x^3+ 3x^2+6x+1)/ ((1-x^3)^2(1-x^2)^2(1-x)^3),{x,0,40}],x],2] (* or *) LinearRecurrence[ {3,-1,-3,-1,3,6,-6,-3,1,3,1,-3,1},{1,9,29,72,154,294,522,877,1406,2172,3255,4746,6763},40] (* Harvey P. Dale, Jul 18 2021 *)

Formula

G.f.: x^2*(x^11-x^10-3*x^9+4*x^7+6*x^6-3*x^5-5*x^4-3*x^3+3*x^2+6*x+1)/((1-x^3)^2*(1-x^2)^2*(1-x)^3).

Extensions

More terms from James Sellers, Jul 04 2000